Actual source code: ex73.c
petsc-3.12.4 2020-02-04
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      1: /*T
      2:    Concepts: KSP^solving a system of linear equations
      3:    Concepts: KSP^Laplacian, 2d
      4:    Processors: n
      5: T*/

      7: /*
      8: This example was derived from src/ksp/ksp/examples/tutorials ex29.c
      9:
     10: Inhomogeneous Laplacian in 2D. Modeled by the partial differential equation

     12:    -div \rho grad u = f,  0 < x,y < 1,

     14: with forcing function

     16:    f = e^{-x^2/\nu} e^{-y^2/\nu}

     18: with Dirichlet boundary conditions

     20:    u = f(x,y) for x = 0, x = 1, y = 0, y = 1

     22: or pure Neumman boundary conditions.
     23: */

     25: static char help[] = "Solves 2D inhomogeneous Laplacian. Demonstates using PCTelescopeSetCoarseDM functionality of PCTelescope via a DMShell\n\n";

     27:  #include <petscdm.h>
     28:  #include <petscdmda.h>
     29:  #include <petscdmshell.h>
     30:  #include <petscksp.h>

     32: PetscErrorCode ComputeMatrix_ShellDA(KSP,Mat,Mat,void*);
     33: PetscErrorCode ComputeMatrix_DMDA(DM,Mat,Mat,void*);
     34: PetscErrorCode ComputeRHS_DMDA(DM,Vec,void*);
     35: PetscErrorCode DMShellCreate_ShellDA(DM,DM*);
     36: PetscErrorCode DMFieldScatter_ShellDA(DM,Vec,ScatterMode,DM,Vec);
     37: PetscErrorCode DMStateScatter_ShellDA(DM,ScatterMode,DM);

     39: typedef enum {DIRICHLET, NEUMANN} BCType;

     41: typedef struct {
     42:   PetscReal rho;
     43:   PetscReal nu;
     44:   BCType    bcType;
     45:   MPI_Comm  comm;
     46: } UserContext;

     49: PetscErrorCode UserContextCreate(MPI_Comm comm,UserContext **ctx)
     50: {
     51:   UserContext    *user;
     52:   const char     *bcTypes[2] = {"dirichlet","neumann"};
     53:   PetscInt       bc;

     57:   PetscCalloc1(1,&user);
     58:   user->comm = comm;
     59:   PetscOptionsBegin(comm, "", "Options for the inhomogeneous Poisson equation", "DMqq");
     60:   user->rho = 1.0;
     61:   PetscOptionsReal("-rho", "The conductivity", "ex29.c", user->rho, &user->rho, NULL);
     62:   user->nu = 0.1;
     63:   PetscOptionsReal("-nu", "The width of the Gaussian source", "ex29.c", user->nu, &user->nu, NULL);
     64:   bc = (PetscInt)DIRICHLET;
     65:   PetscOptionsEList("-bc_type","Type of boundary condition","ex29.c",bcTypes,2,bcTypes[0],&bc,NULL);
     66:   user->bcType = (BCType)bc;
     67:   PetscOptionsEnd();
     68:   *ctx = user;
     69:   return(0);
     70: }

     72: PetscErrorCode CommCoarsen(MPI_Comm comm,PetscInt number,PetscSubcomm *p)
     73: {
     74:   PetscSubcomm   psubcomm;
     77:   PetscSubcommCreate(comm,&psubcomm);
     78:   PetscSubcommSetNumber(psubcomm,number);
     79:   PetscSubcommSetType(psubcomm,PETSC_SUBCOMM_INTERLACED);
     80:   *p = psubcomm;
     81:   return(0);
     82: }

     84: PetscErrorCode CommHierarchyCreate(MPI_Comm comm,PetscInt n,PetscInt number[],PetscSubcomm pscommlist[])
     85: {
     86:   PetscInt       k;
     87:   PetscBool      view_hierarchy = PETSC_FALSE;

     91:   for (k=0; k<n; k++) {
     92:     pscommlist[k] = NULL;
     93:   }

     95:   if (n < 1) return(0);

     97:   CommCoarsen(comm,number[n-1],&pscommlist[n-1]);
     98:   for (k=n-2; k>=0; k--) {
     99:     MPI_Comm comm_k = PetscSubcommChild(pscommlist[k+1]);
    100:     if (pscommlist[k+1]->color == 0) {
    101:       CommCoarsen(comm_k,number[k],&pscommlist[k]);
    102:     }
    103:   }

    105:   PetscOptionsGetBool(NULL,NULL,"-view_hierarchy",&view_hierarchy,NULL);
    106:   if (view_hierarchy) {
    107:     PetscMPIInt size;

    109:     MPI_Comm_size(comm,&size);
    110:     PetscPrintf(comm,"level[%D] size %d\n",n,(int)size);
    111:     for (k=n-1; k>=0; k--) {
    112:       if (pscommlist[k]) {
    113:         MPI_Comm comm_k = PetscSubcommChild(pscommlist[k]);

    115:         if (pscommlist[k]->color == 0) {
    116:           MPI_Comm_size(comm_k,&size);
    117:           PetscPrintf(comm_k,"level[%D] size %d\n",k,(int)size);
    118:         }
    119:       }
    120:     }
    121:   }
    122:   return(0);
    123: }

    125: /* taken from src/ksp/pc/impls/telescope/telescope_dmda.c */
    126: static PetscErrorCode _DMDADetermineRankFromGlobalIJ_2d(PetscInt i,PetscInt j,PetscInt Mp,PetscInt Np,
    127:                                                         PetscInt start_i[],PetscInt start_j[],
    128:                                                         PetscInt span_i[],PetscInt span_j[],
    129:                                                         PetscMPIInt *_pi,PetscMPIInt *_pj,PetscMPIInt *rank_re)
    130: {
    131:   PetscInt pi,pj,n;

    134:   *rank_re = -1;
    135:   pi = pj = -1;
    136:   if (_pi) {
    137:     for (n=0; n<Mp; n++) {
    138:       if ( (i >= start_i[n]) && (i < start_i[n]+span_i[n]) ) {
    139:         pi = n;
    140:         break;
    141:       }
    142:     }
    143:     if (pi == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_USER,"[dmda-ij] pi cannot be determined : range %D, val %D",Mp,i);
    144:     *_pi = (PetscMPIInt)pi;
    145:   }

    147:   if (_pj) {
    148:     for (n=0; n<Np; n++) {
    149:       if ( (j >= start_j[n]) && (j < start_j[n]+span_j[n]) ) {
    150:         pj = n;
    151:         break;
    152:       }
    153:     }
    154:     if (pj == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_USER,"[dmda-ij] pj cannot be determined : range %D, val %D",Np,j);
    155:     *_pj = (PetscMPIInt)pj;
    156:   }

    158:   *rank_re = (PetscMPIInt)(pi + pj * Mp);
    159:   return(0);
    160: }

    162: /* taken from src/ksp/pc/impls/telescope/telescope_dmda.c */
    163: static PetscErrorCode _DMDADetermineGlobalS0_2d(PetscMPIInt rank_re,PetscInt Mp_re,PetscInt Np_re,
    164:                                                 PetscInt range_i_re[],PetscInt range_j_re[],PetscInt *s0)
    165: {
    166:   PetscInt    i,j,start_IJ = 0;
    167:   PetscMPIInt rank_ij;

    170:   *s0 = -1;
    171:   for (j=0; j<Np_re; j++) {
    172:     for (i=0; i<Mp_re; i++) {
    173:       rank_ij = (PetscMPIInt)(i + j*Mp_re);
    174:       if (rank_ij < rank_re) {
    175:         start_IJ += range_i_re[i]*range_j_re[j];
    176:       }
    177:     }
    178:   }
    179:   *s0 = start_IJ;
    180:   return(0);
    181: }

    183: /* adapted from src/ksp/pc/impls/telescope/telescope_dmda.c */
    184: static PetscErrorCode DMDACreatePermutation_2d(DM dmrepart,DM dmf,Mat *mat)
    185: {
    187:   PetscInt       k,sum,Mp_re = 0,Np_re = 0;
    188:   PetscInt       nx,ny,sr,er,Mr,ndof;
    189:   PetscInt       i,j,location,startI[2],endI[2],lenI[2];
    190:   const PetscInt *_range_i_re = NULL,*_range_j_re = NULL;
    191:   PetscInt       *range_i_re,*range_j_re;
    192:   PetscInt       *start_i_re,*start_j_re;
    193:   MPI_Comm       comm;
    194:   Vec            V;
    195:   Mat            Pscalar;

    198:   PetscInfo(dmf,"setting up the permutation matrix (DMDA-2D)\n");
    199:   PetscObjectGetComm((PetscObject)dmf,&comm);

    201:   _range_i_re = _range_j_re = NULL;
    202:   /* Create DMDA on the child communicator */
    203:   if (dmrepart) {
    204:     DMDAGetInfo(dmrepart,NULL,NULL,NULL,NULL,&Mp_re,&Np_re,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
    205:     DMDAGetOwnershipRanges(dmrepart,&_range_i_re,&_range_j_re,NULL);
    206:   }

    208:   /* note - assume rank 0 always participates */
    209:   MPI_Bcast(&Mp_re,1,MPIU_INT,0,comm);
    210:   MPI_Bcast(&Np_re,1,MPIU_INT,0,comm);

    212:   PetscCalloc1(Mp_re,&range_i_re);
    213:   PetscCalloc1(Np_re,&range_j_re);

    215:   if (_range_i_re) {PetscArraycpy(range_i_re,_range_i_re,Mp_re);}
    216:   if (_range_j_re) {PetscArraycpy(range_j_re,_range_j_re,Np_re);}

    218:   MPI_Bcast(range_i_re,Mp_re,MPIU_INT,0,comm);
    219:   MPI_Bcast(range_j_re,Np_re,MPIU_INT,0,comm);

    221:   PetscMalloc1(Mp_re,&start_i_re);
    222:   PetscMalloc1(Np_re,&start_j_re);

    224:   sum = 0;
    225:   for (k=0; k<Mp_re; k++) {
    226:     start_i_re[k] = sum;
    227:     sum += range_i_re[k];
    228:   }

    230:   sum = 0;
    231:   for (k=0; k<Np_re; k++) {
    232:     start_j_re[k] = sum;
    233:     sum += range_j_re[k];
    234:   }

    236:   /* Create permutation */
    237:   DMDAGetInfo(dmf,NULL,&nx,&ny,NULL,NULL,NULL,NULL,&ndof,NULL,NULL,NULL,NULL,NULL);
    238:   DMGetGlobalVector(dmf,&V);
    239:   VecGetSize(V,&Mr);
    240:   VecGetOwnershipRange(V,&sr,&er);
    241:   DMRestoreGlobalVector(dmf,&V);
    242:   sr = sr / ndof;
    243:   er = er / ndof;
    244:   Mr = Mr / ndof;

    246:   MatCreate(comm,&Pscalar);
    247:   MatSetSizes(Pscalar,(er-sr),(er-sr),Mr,Mr);
    248:   MatSetType(Pscalar,MATAIJ);
    249:   MatSeqAIJSetPreallocation(Pscalar,1,NULL);
    250:   MatMPIAIJSetPreallocation(Pscalar,1,NULL,1,NULL);

    252:   DMDAGetCorners(dmf,NULL,NULL,NULL,&lenI[0],&lenI[1],NULL);
    253:   DMDAGetCorners(dmf,&startI[0],&startI[1],NULL,&endI[0],&endI[1],NULL);
    254:   endI[0] += startI[0];
    255:   endI[1] += startI[1];

    257:   for (j=startI[1]; j<endI[1]; j++) {
    258:     for (i=startI[0]; i<endI[0]; i++) {
    259:       PetscMPIInt rank_ijk_re,rank_reI[] = {0,0};
    260:       PetscInt    s0_re;
    261:       PetscInt    ii,jj,local_ijk_re,mapped_ijk;
    262:       PetscInt    lenI_re[] = {0,0};

    264:       location = (i - startI[0]) + (j - startI[1])*lenI[0];
    265:       _DMDADetermineRankFromGlobalIJ_2d(i,j,Mp_re,Np_re,
    266:                                              start_i_re,start_j_re,
    267:                                              range_i_re,range_j_re,
    268:                                              &rank_reI[0],&rank_reI[1],&rank_ijk_re);

    270:       _DMDADetermineGlobalS0_2d(rank_ijk_re,Mp_re,Np_re,range_i_re,range_j_re,&s0_re);

    272:       ii = i - start_i_re[ rank_reI[0] ];
    273:       if (ii < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"[dmdarepart-perm2d] index error ii");
    274:       jj = j - start_j_re[ rank_reI[1] ];
    275:       if (jj < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"[dmdarepart-perm2d] index error jj");

    277:       lenI_re[0] = range_i_re[ rank_reI[0] ];
    278:       lenI_re[1] = range_j_re[ rank_reI[1] ];
    279:       local_ijk_re = ii + jj * lenI_re[0];
    280:       mapped_ijk = s0_re + local_ijk_re;
    281:       MatSetValue(Pscalar,sr+location,mapped_ijk,1.0,INSERT_VALUES);
    282:     }
    283:   }
    284:   MatAssemblyBegin(Pscalar,MAT_FINAL_ASSEMBLY);
    285:   MatAssemblyEnd(Pscalar,MAT_FINAL_ASSEMBLY);

    287:   *mat = Pscalar;

    289:   PetscFree(range_i_re);
    290:   PetscFree(range_j_re);
    291:   PetscFree(start_i_re);
    292:   PetscFree(start_j_re);
    293:   return(0);
    294: }

    296: /* adapted from src/ksp/pc/impls/telescope/telescope_dmda.c */
    297: static PetscErrorCode PCTelescopeSetUp_dmda_scatters(DM dmf,DM dmc)
    298: {
    300:   Vec            xred,yred,xtmp,x,xp;
    301:   VecScatter     scatter;
    302:   IS             isin;
    303:   PetscInt       m,bs,st,ed;
    304:   MPI_Comm       comm;
    305:   VecType        vectype;

    308:   PetscObjectGetComm((PetscObject)dmf,&comm);
    309:   DMCreateGlobalVector(dmf,&x);
    310:   VecGetBlockSize(x,&bs);
    311:   VecGetType(x,&vectype);

    313:   /* cannot use VecDuplicate as xp is already composed with dmf */
    314:   /*VecDuplicate(x,&xp);*/
    315:   {
    316:     PetscInt m,M;

    318:     VecGetSize(x,&M);
    319:     VecGetLocalSize(x,&m);
    320:     VecCreate(comm,&xp);
    321:     VecSetSizes(xp,m,M);
    322:     VecSetBlockSize(xp,bs);
    323:     VecSetType(xp,vectype);
    324:   }

    326:   m = 0;
    327:   xred = NULL;
    328:   yred = NULL;
    329:   if (dmc) {
    330:     DMCreateGlobalVector(dmc,&xred);
    331:     VecDuplicate(xred,&yred);
    332:     VecGetOwnershipRange(xred,&st,&ed);
    333:     ISCreateStride(comm,ed-st,st,1,&isin);
    334:     VecGetLocalSize(xred,&m);
    335:   } else {
    336:     VecGetOwnershipRange(x,&st,&ed);
    337:     ISCreateStride(comm,0,st,1,&isin);
    338:   }
    339:   ISSetBlockSize(isin,bs);
    340:   VecCreate(comm,&xtmp);
    341:   VecSetSizes(xtmp,m,PETSC_DECIDE);
    342:   VecSetBlockSize(xtmp,bs);
    343:   VecSetType(xtmp,vectype);
    344:   VecScatterCreate(x,isin,xtmp,NULL,&scatter);

    346:   PetscObjectCompose((PetscObject)dmf,"isin",(PetscObject)isin);
    347:   PetscObjectCompose((PetscObject)dmf,"scatter",(PetscObject)scatter);
    348:   PetscObjectCompose((PetscObject)dmf,"xtmp",(PetscObject)xtmp);
    349:   PetscObjectCompose((PetscObject)dmf,"xp",(PetscObject)xp);

    351:   VecDestroy(&xred);
    352:   VecDestroy(&yred);
    353:   VecDestroy(&x);
    354:   return(0);
    355: }

    357: PetscErrorCode DMCreateMatrix_ShellDA(DM dm,Mat *A)
    358: {
    359:   DM             da;
    360:   MPI_Comm       comm;
    361:   PetscMPIInt    size;
    362:   UserContext    *ctx = NULL;
    363:   PetscInt       M,N;

    367:   DMShellGetContext(dm,(void**)&da);
    368:   PetscObjectGetComm((PetscObject)da,&comm);
    369:   MPI_Comm_size(comm,&size);
    370:   DMCreateMatrix(da,A);
    371:   MatGetSize(*A,&M,&N);
    372:   PetscPrintf(comm,"[size %D] DMCreateMatrix_ShellDA (%D x %D)\n",(PetscInt)size,M,N);

    374:   DMGetApplicationContext(dm,(void*)&ctx);
    375:   if (ctx->bcType == NEUMANN) {
    376:     MatNullSpace nullspace = NULL;
    377:     PetscPrintf(comm,"[size %D] DMCreateMatrix_ShellDA: using neumann bcs\n",(PetscInt)size);

    379:     MatGetNullSpace(*A,&nullspace);
    380:     if (!nullspace) {
    381:       PetscPrintf(comm,"[size %D] DMCreateMatrix_ShellDA: operator does not have nullspace - attaching\n",(PetscInt)size);
    382:       MatNullSpaceCreate(comm,PETSC_TRUE,0,0,&nullspace);
    383:       MatSetNullSpace(*A,nullspace);
    384:       MatNullSpaceDestroy(&nullspace);
    385:     } else {
    386:       PetscPrintf(comm,"[size %D] DMCreateMatrix_ShellDA: operator already has a nullspace\n",(PetscInt)size);
    387:     }
    388:   }
    389:   return(0);
    390: }

    392: PetscErrorCode DMCreateGlobalVector_ShellDA(DM dm,Vec *x)
    393: {
    394:   DM             da;
    397:   DMShellGetContext(dm,(void**)&da);
    398:   DMCreateGlobalVector(da,x);
    399:   VecSetDM(*x,dm);
    400:   return(0);
    401: }

    403: PetscErrorCode DMCreateLocalVector_ShellDA(DM dm,Vec *x)
    404: {
    405:   DM             da;
    408:   DMShellGetContext(dm,(void**)&da);
    409:   DMCreateLocalVector(da,x);
    410:   VecSetDM(*x,dm);
    411:   return(0);
    412: }

    414: PetscErrorCode DMCoarsen_ShellDA(DM dm,MPI_Comm comm,DM *dmc)
    415: {
    418:   *dmc = NULL;
    419:   DMGetCoarseDM(dm,dmc);
    420:   if (!*dmc) {
    421:     SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"The coarse DM should never be NULL. The DM hierarchy should have already been defined");
    422:   } else {
    423:     PetscObjectReference((PetscObject)(*dmc));
    424:   }
    425:   return(0);
    426: }

    428: PetscErrorCode DMCreateInterpolation_ShellDA(DM dm1,DM dm2,Mat *mat,Vec *vec)
    429: {
    430:   DM             da1,da2;
    433:   DMShellGetContext(dm1,(void**)&da1);
    434:   DMShellGetContext(dm2,(void**)&da2);
    435:   DMCreateInterpolation(da1,da2,mat,vec);
    436:   return(0);
    437: }

    439: PetscErrorCode DMShellDASetUp_TelescopeDMScatter(DM dmf_shell,DM dmc_shell)
    440: {
    442:   Mat            P = NULL;
    443:   DM             dmf = NULL,dmc = NULL;

    446:   DMShellGetContext(dmf_shell,(void**)&dmf);
    447:   if (dmc_shell) {
    448:     DMShellGetContext(dmc_shell,(void**)&dmc);
    449:   }
    450:   DMDACreatePermutation_2d(dmc,dmf,&P);
    451:   PetscObjectCompose((PetscObject)dmf,"P",(PetscObject)P);
    452:   PCTelescopeSetUp_dmda_scatters(dmf,dmc);
    453:   PetscObjectComposeFunction((PetscObject)dmf_shell,"PCTelescopeFieldScatter",DMFieldScatter_ShellDA);
    454:   PetscObjectComposeFunction((PetscObject)dmf_shell,"PCTelescopeStateScatter",DMStateScatter_ShellDA);
    455:   return(0);
    456: }

    458: PetscErrorCode DMShellDAFieldScatter_Forward(DM dmf,Vec x,DM dmc,Vec xc)
    459: {
    460:   PetscErrorCode    ierr;
    461:   Mat               P = NULL;
    462:   Vec               xp = NULL,xtmp = NULL;
    463:   VecScatter        scatter = NULL;
    464:   const PetscScalar *x_array;
    465:   PetscInt          i,st,ed;

    468:   PetscObjectQuery((PetscObject)dmf,"P",(PetscObject*)&P);
    469:   PetscObjectQuery((PetscObject)dmf,"xp",(PetscObject*)&xp);
    470:   PetscObjectQuery((PetscObject)dmf,"scatter",(PetscObject*)&scatter);
    471:   PetscObjectQuery((PetscObject)dmf,"xtmp",(PetscObject*)&xtmp);
    472:   if (!P) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Require a permutation matrix (\"P\")to be composed with the parent (fine) DM");
    473:   if (!xp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Require \"xp\" to be composed with the parent (fine) DM");
    474:   if (!scatter) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Require \"scatter\" to be composed with the parent (fine) DM");
    475:   if (!xtmp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Require \"xtmp\" to be composed with the parent (fine) DM");

    477:   MatMultTranspose(P,x,xp);

    479:   /* pull in vector x->xtmp */
    480:   VecScatterBegin(scatter,xp,xtmp,INSERT_VALUES,SCATTER_FORWARD);
    481:   VecScatterEnd(scatter,xp,xtmp,INSERT_VALUES,SCATTER_FORWARD);

    483:   /* copy vector entires into xred */
    484:   VecGetArrayRead(xtmp,&x_array);
    485:   if (xc) {
    486:     PetscScalar *LA_xred;
    487:     VecGetOwnershipRange(xc,&st,&ed);

    489:     VecGetArray(xc,&LA_xred);
    490:     for (i=0; i<ed-st; i++) {
    491:       LA_xred[i] = x_array[i];
    492:     }
    493:     VecRestoreArray(xc,&LA_xred);
    494:   }
    495:   VecRestoreArrayRead(xtmp,&x_array);
    496:   return(0);
    497: }

    499: PetscErrorCode DMShellDAFieldScatter_Reverse(DM dmf,Vec y,DM dmc,Vec yc)
    500: {
    502:   Mat            P = NULL;
    503:   Vec            xp = NULL,xtmp = NULL;
    504:   VecScatter     scatter = NULL;
    505:   PetscScalar    *array;
    506:   PetscInt       i,st,ed;

    509:   PetscObjectQuery((PetscObject)dmf,"P",(PetscObject*)&P);
    510:   PetscObjectQuery((PetscObject)dmf,"xp",(PetscObject*)&xp);
    511:   PetscObjectQuery((PetscObject)dmf,"scatter",(PetscObject*)&scatter);
    512:   PetscObjectQuery((PetscObject)dmf,"xtmp",(PetscObject*)&xtmp);

    514:   if (!P) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Require a permutation matrix (\"P\")to be composed with the parent (fine) DM");
    515:   if (!xp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Require \"xp\" to be composed with the parent (fine) DM");
    516:   if (!scatter) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Require \"scatter\" to be composed with the parent (fine) DM");
    517:   if (!xtmp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Require \"xtmp\" to be composed with the parent (fine) DM");

    519:   /* return vector */
    520:   VecGetArray(xtmp,&array);
    521:   if (yc) {
    522:     const PetscScalar *LA_yred;
    523:     VecGetOwnershipRange(yc,&st,&ed);
    524:     VecGetArrayRead(yc,&LA_yred);
    525:     for (i=0; i<ed-st; i++) {
    526:       array[i] = LA_yred[i];
    527:     }
    528:     VecRestoreArrayRead(yc,&LA_yred);
    529:   }
    530:   VecRestoreArray(xtmp,&array);
    531:   VecScatterBegin(scatter,xtmp,xp,INSERT_VALUES,SCATTER_REVERSE);
    532:   VecScatterEnd(scatter,xtmp,xp,INSERT_VALUES,SCATTER_REVERSE);
    533:   MatMult(P,xp,y);
    534:   return(0);
    535: }

    537: PetscErrorCode DMFieldScatter_ShellDA(DM dmf_shell,Vec x,ScatterMode mode,DM dmc_shell,Vec xc)
    538: {
    540:   DM             dmf = NULL,dmc = NULL;

    543:   DMShellGetContext(dmf_shell,(void**)&dmf);
    544:   if (dmc_shell) {
    545:     DMShellGetContext(dmc_shell,(void**)&dmc);
    546:   }
    547:   if (mode == SCATTER_FORWARD) {
    548:     DMShellDAFieldScatter_Forward(dmf,x,dmc,xc);
    549:   } else if (mode == SCATTER_REVERSE) {
    550:     DMShellDAFieldScatter_Reverse(dmf,x,dmc,xc);
    551:   } else SETERRQ(PetscObjectComm((PetscObject)dmf_shell),PETSC_ERR_SUP,"Only mode = SCATTER_FORWARD, SCATTER_REVERSE supported");
    552:   return(0);
    553: }

    555: PetscErrorCode DMStateScatter_ShellDA(DM dmf_shell,ScatterMode mode,DM dmc_shell)
    556: {
    557:   PetscMPIInt    size_f = 0,size_c = 0;
    560:   MPI_Comm_size(PetscObjectComm((PetscObject)dmf_shell),&size_f);
    561:   if (dmc_shell) {
    562:     MPI_Comm_size(PetscObjectComm((PetscObject)dmc_shell),&size_c);
    563:   }
    564:   if (mode == SCATTER_FORWARD) {
    565:     PetscPrintf(PetscObjectComm((PetscObject)dmf_shell),"User supplied state scatter (fine [size %d]-> coarse [size %d])\n",(int)size_f,(int)size_c);
    566:   } else if (mode == SCATTER_REVERSE) {
    567:   } else SETERRQ(PetscObjectComm((PetscObject)dmf_shell),PETSC_ERR_SUP,"Only mode = SCATTER_FORWARD, SCATTER_REVERSE supported");
    568:   return(0);
    569: }

    571: PetscErrorCode DMShellCreate_ShellDA(DM da,DM *dms)
    572: {
    575:   if (da) {
    576:     DMShellCreate(PetscObjectComm((PetscObject)da),dms);
    577:     DMShellSetContext(*dms,(void*)da);
    578:     DMShellSetCreateGlobalVector(*dms,DMCreateGlobalVector_ShellDA);
    579:     DMShellSetCreateLocalVector(*dms,DMCreateLocalVector_ShellDA);
    580:     DMShellSetCreateMatrix(*dms,DMCreateMatrix_ShellDA);
    581:     DMShellSetCoarsen(*dms,DMCoarsen_ShellDA);
    582:     DMShellSetCreateInterpolation(*dms,DMCreateInterpolation_ShellDA);
    583:   } else {
    584:     *dms = NULL;
    585:   }
    586:   return(0);
    587: }

    589: PetscErrorCode DMDestroyShellDMDA(DM *_dm)
    590: {
    592:   DM             dm,da = NULL;

    595:   if (!_dm) return(0);
    596:   dm = *_dm;
    597:   if (!dm) return(0);

    599:   DMShellGetContext(dm,(void**)&da);
    600:   if (da) {
    601:     Vec        vec;
    602:     VecScatter scatter = NULL;
    603:     IS         is = NULL;
    604:     Mat        P = NULL;

    606:     PetscObjectQuery((PetscObject)da,"P",(PetscObject*)&P);
    607:     MatDestroy(&P);

    609:     vec = NULL;
    610:     PetscObjectQuery((PetscObject)da,"xp",(PetscObject*)&vec);
    611:     VecDestroy(&vec);

    613:     PetscObjectQuery((PetscObject)da,"scatter",(PetscObject*)&scatter);
    614:     VecScatterDestroy(&scatter);

    616:     vec = NULL;
    617:     PetscObjectQuery((PetscObject)da,"xtmp",(PetscObject*)&vec);
    618:     VecDestroy(&vec);

    620:     PetscObjectQuery((PetscObject)da,"isin",(PetscObject*)&is);
    621:     ISDestroy(&is);

    623:     DMDestroy(&da);
    624:   }
    625:   DMDestroy(&dm);
    626:   *_dm = NULL;
    627:   return(0);
    628: }

    630: PetscErrorCode HierarchyCreate_Basic(DM *dm_f,DM *dm_c,UserContext *ctx)
    631: {
    633:   DM             dm,dmc,dm_shell,dmc_shell;
    634:   PetscMPIInt    rank;

    637:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
    638:   DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,17,17,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&dm);
    639:   DMSetFromOptions(dm);
    640:   DMSetUp(dm);
    641:   DMDASetUniformCoordinates(dm,0,1,0,1,0,0);
    642:   DMDASetFieldName(dm,0,"Pressure");
    643:   DMShellCreate_ShellDA(dm,&dm_shell);
    644:   DMSetApplicationContext(dm_shell,(void*)ctx);

    646:   dmc = NULL;
    647:   dmc_shell = NULL;
    648:   if (!rank) {
    649:     DMDACreate2d(PETSC_COMM_SELF,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,17,17,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&dmc);
    650:     DMSetFromOptions(dmc);
    651:     DMSetUp(dmc);
    652:     DMDASetUniformCoordinates(dmc,0,1,0,1,0,0);
    653:     DMDASetFieldName(dmc,0,"Pressure");
    654:     DMShellCreate_ShellDA(dmc,&dmc_shell);
    655:     DMSetApplicationContext(dmc_shell,(void*)ctx);
    656:   }

    658:   DMSetCoarseDM(dm_shell,dmc_shell);
    659:   DMShellDASetUp_TelescopeDMScatter(dm_shell,dmc_shell);

    661:   *dm_f = dm_shell;
    662:   *dm_c = dmc_shell;
    663:   return(0);
    664: }

    666: PetscErrorCode HierarchyCreate(PetscInt *_nd,PetscInt *_nref,MPI_Comm **_cl,DM **_dl)
    667: {
    668:   PetscInt       d,k,ndecomps,ncoarsen,found,nx;
    669:   PetscInt       levelrefs,*number;
    670:   PetscSubcomm   *pscommlist;
    671:   MPI_Comm       *commlist;
    672:   DM             *dalist,*dmlist;
    673:   PetscBool      set;

    677:   ndecomps = 1;
    678:   PetscOptionsGetInt(NULL,NULL,"-ndecomps",&ndecomps,NULL);
    679:   ncoarsen = ndecomps - 1;
    680:   if (ncoarsen < 0) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER,"-ndecomps must be >= 1");

    682:   levelrefs = 2;
    683:   PetscOptionsGetInt(NULL,NULL,"-level_nrefs",&levelrefs,NULL);
    684:   PetscMalloc1(ncoarsen+1,&number);
    685:   for (k=0; k<ncoarsen+1; k++) {
    686:     number[k] = 2;
    687:   }
    688:   found = ncoarsen;
    689:   set = PETSC_FALSE;
    690:   PetscOptionsGetIntArray(NULL,NULL,"-level_comm_red_factor",number,&found,&set);
    691:   if (set) {
    692:     if (found != ncoarsen) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_USER,"Expected %D values for -level_comm_red_factor. Found %D",ncoarsen,found);
    693:   }

    695:   PetscMalloc1(ncoarsen+1,&pscommlist);
    696:   for (k=0; k<ncoarsen+1; k++) {
    697:     pscommlist[k] = NULL;
    698:   }

    700:   PetscMalloc1(ndecomps,&commlist);
    701:   for (k=0; k<ndecomps; k++) {
    702:     commlist[k] = MPI_COMM_NULL;
    703:   }
    704:   PetscMalloc1(ndecomps*levelrefs,&dalist);
    705:   PetscMalloc1(ndecomps*levelrefs,&dmlist);
    706:   for (k=0; k<ndecomps*levelrefs; k++) {
    707:     dalist[k] = NULL;
    708:     dmlist[k] = NULL;
    709:   }

    711:   CommHierarchyCreate(PETSC_COMM_WORLD,ncoarsen,number,pscommlist);
    712:   for (k=0; k<ncoarsen; k++) {
    713:     if (pscommlist[k]) {
    714:       MPI_Comm comm_k = PetscSubcommChild(pscommlist[k]);
    715:       if (pscommlist[k]->color == 0) {
    716:         PetscCommDuplicate(comm_k,&commlist[k],NULL);
    717:       }
    718:     }
    719:   }
    720:   PetscCommDuplicate(PETSC_COMM_WORLD,&commlist[ndecomps-1],NULL);

    722:   for (k=0; k<ncoarsen; k++) {
    723:     if (pscommlist[k]) {
    724:       PetscSubcommDestroy(&pscommlist[k]);
    725:     }
    726:   }

    728:   nx = 17;
    729:   PetscOptionsGetInt(NULL,NULL,"-m",&nx,NULL);
    730:   for (d=0; d<ndecomps; d++) {
    731:     DM   dmroot = NULL;
    732:     char name[PETSC_MAX_PATH_LEN];

    734:     if (commlist[d] != MPI_COMM_NULL) {
    735:       DMDACreate2d(commlist[d],DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,nx,nx,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&dmroot);
    736:       DMSetUp(dmroot);
    737:       DMDASetUniformCoordinates(dmroot,0,1,0,1,0,0);
    738:       DMDASetFieldName(dmroot,0,"Pressure");
    739:       PetscSNPrintf(name,PETSC_MAX_PATH_LEN-1,"root-decomp-%D",d);
    740:       PetscObjectSetName((PetscObject)dmroot,name);
    741:       /*DMView(dmroot,PETSC_VIEWER_STDOUT_(commlist[d]));*/
    742:     }

    744:     dalist[d*levelrefs + 0] = dmroot;
    745:     for (k=1; k<levelrefs; k++) {
    746:       DM dmref = NULL;

    748:       if (commlist[d] != MPI_COMM_NULL) {
    749:         DMRefine(dalist[d*levelrefs + (k-1)],MPI_COMM_NULL,&dmref);
    750:         PetscSNPrintf(name,PETSC_MAX_PATH_LEN-1,"ref%D-decomp-%D",k,d);
    751:         PetscObjectSetName((PetscObject)dmref,name);
    752:         DMDAGetInfo(dmref,NULL,&nx,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
    753:         /*DMView(dmref,PETSC_VIEWER_STDOUT_(commlist[d]));*/
    754:       }
    755:       dalist[d*levelrefs + k] = dmref;
    756:     }
    757:     MPI_Allreduce(MPI_IN_PLACE,&nx,1,MPIU_INT,MPI_MAX,PETSC_COMM_WORLD);
    758:   }

    760:   /* create the hierarchy of DMShell's */
    761:   for (d=0; d<ndecomps; d++) {
    762:     char name[PETSC_MAX_PATH_LEN];

    764:     UserContext *ctx = NULL;
    765:     if (commlist[d] != MPI_COMM_NULL) {
    766:       UserContextCreate(commlist[d],&ctx);
    767:       for (k=0; k<levelrefs; k++) {
    768:         DMShellCreate_ShellDA(dalist[d*levelrefs + k],&dmlist[d*levelrefs + k]);
    769:         DMSetApplicationContext(dmlist[d*levelrefs + k],(void*)ctx);
    770:         PetscSNPrintf(name,PETSC_MAX_PATH_LEN-1,"level%D-decomp-%D",k,d);
    771:         PetscObjectSetName((PetscObject)dmlist[d*levelrefs + k],name);
    772:       }
    773:     }
    774:   }

    776:   /* set all the coarse DMs */
    777:   for (k=1; k<ndecomps*levelrefs; k++) { /* skip first DM as it doesn't have a coarse representation */
    778:     DM dmfine = NULL,dmcoarse = NULL;

    780:     dmfine = dmlist[k];
    781:     dmcoarse = dmlist[k-1];
    782:     if (dmfine) {
    783:       DMSetCoarseDM(dmfine,dmcoarse);
    784:     }
    785:   }

    787:   /* do special setup on the fine DM coupling different decompositions */
    788:   for (d=1; d<ndecomps; d++) { /* skip first decomposition as it doesn't have a coarse representation */
    789:     DM dmfine = NULL,dmcoarse = NULL;

    791:     dmfine = dmlist[d*levelrefs + 0];
    792:     dmcoarse = dmlist[(d-1)*levelrefs + (levelrefs-1)];
    793:     if (dmfine) {
    794:       DMShellDASetUp_TelescopeDMScatter(dmfine,dmcoarse);
    795:     }
    796:   }

    798:   PetscFree(number);
    799:   for (k=0; k<ncoarsen; k++) {
    800:     PetscSubcommDestroy(&pscommlist[k]);
    801:   }
    802:   PetscFree(pscommlist);

    804:   if (_nd) {
    805:     *_nd = ndecomps;
    806:   }
    807:   if (_nref) {
    808:     *_nref = levelrefs;
    809:   }
    810:   if (_cl) {
    811:     *_cl = commlist;
    812:   } else {
    813:     for (k=0; k<ndecomps; k++) {
    814:       if (commlist[k] != MPI_COMM_NULL) {
    815:         PetscCommDestroy(&commlist[k]);
    816:       }
    817:     }
    818:     PetscFree(commlist);
    819:   }
    820:   if (_dl) {
    821:     *_dl = dmlist;
    822:     PetscFree(dalist);
    823:   } else {
    824:     for (k=0; k<ndecomps*levelrefs; k++) {
    825:       DMDestroy(&dmlist[k]);
    826:       DMDestroy(&dalist[k]);
    827:     }
    828:     PetscFree(dmlist);
    829:     PetscFree(dalist);
    830:   }
    831:   return(0);
    832: }

    834: PetscErrorCode test_hierarchy(void)
    835: {
    837:   PetscInt       d,k,nd,nref;
    838:   MPI_Comm       *comms;
    839:   DM             *dms;

    842:   HierarchyCreate(&nd,&nref,&comms,&dms);

    844:   /* destroy user context */
    845:   for (d=0; d<nd; d++) {
    846:     DM first = dms[d*nref+0];

    848:     if (first) {
    849:       UserContext *ctx = NULL;

    851:       DMGetApplicationContext(first,(void*)&ctx);
    852:       if (ctx) { PetscFree(ctx); }
    853:       DMSetApplicationContext(first,NULL);
    854:     }
    855:     for (k=1; k<nref; k++) {
    856:       DM dm = dms[d*nref+k];
    857:       if (dm) {
    858:         DMSetApplicationContext(dm,NULL);
    859:       }
    860:     }
    861:   }

    863:   /* destroy DMs */
    864:   for (k=0; k<nd*nref; k++) {
    865:     if (dms[k]) {
    866:       DMDestroyShellDMDA(&dms[k]);
    867:     }
    868:   }
    869:   PetscFree(dms);

    871:   /* destroy communicators */
    872:   for (k=0; k<nd; k++) {
    873:     if (comms[k] != MPI_COMM_NULL) {
    874:       PetscCommDestroy(&comms[k]);
    875:     }
    876:   }
    877:   PetscFree(comms);
    878:   return(0);
    879: }

    881: PetscErrorCode test_basic(void)
    882: {
    884:   DM             dmF,dmdaF = NULL,dmC = NULL;
    885:   Mat            A;
    886:   Vec            x,b;
    887:   KSP            ksp;
    888:   PC             pc;
    889:   UserContext    *user = NULL;

    892:   UserContextCreate(PETSC_COMM_WORLD,&user);
    893:   HierarchyCreate_Basic(&dmF,&dmC,user);
    894:   DMShellGetContext(dmF,(void**)&dmdaF);

    896:   DMCreateMatrix(dmF,&A);
    897:   DMCreateGlobalVector(dmF,&x);
    898:   DMCreateGlobalVector(dmF,&b);
    899:   ComputeRHS_DMDA(dmdaF,b,user);

    901:   KSPCreate(PETSC_COMM_WORLD,&ksp);
    902:   KSPSetComputeOperators(ksp,ComputeMatrix_ShellDA,(void*)user);
    903:   /*KSPSetOperators(ksp,A,A);*/
    904:   KSPSetDM(ksp,dmF);
    905:   KSPSetDMActive(ksp,PETSC_TRUE);
    906:   KSPSetFromOptions(ksp);
    907:   KSPGetPC(ksp,&pc);
    908:   PCTelescopeSetUseCoarseDM(pc,PETSC_TRUE);

    910:   KSPSolve(ksp,b,x);

    912:   if (dmC) {
    913:     DMDestroyShellDMDA(&dmC);
    914:   }
    915:   DMDestroyShellDMDA(&dmF);
    916:   KSPDestroy(&ksp);
    917:   MatDestroy(&A);
    918:   VecDestroy(&b);
    919:   VecDestroy(&x);
    920:   PetscFree(user);
    921:   return(0);
    922: }

    924: PetscErrorCode test_mg(void)
    925: {
    927:   DM             dmF,dmdaF = NULL,*dms = NULL;
    928:   Mat            A;
    929:   Vec            x,b;
    930:   KSP            ksp;
    931:   PetscInt       k,d,nd,nref;
    932:   MPI_Comm       *comms = NULL;
    933:   UserContext    *user = NULL;

    936:   HierarchyCreate(&nd,&nref,&comms,&dms);
    937:   dmF = dms[nd*nref-1];

    939:   DMShellGetContext(dmF,(void**)&dmdaF);
    940:   DMGetApplicationContext(dmF,(void*)&user);

    942:   DMCreateMatrix(dmF,&A);
    943:   DMCreateGlobalVector(dmF,&x);
    944:   DMCreateGlobalVector(dmF,&b);
    945:   ComputeRHS_DMDA(dmdaF,b,user);

    947:   KSPCreate(PETSC_COMM_WORLD,&ksp);
    948:   KSPSetComputeOperators(ksp,ComputeMatrix_ShellDA,(void*)user);
    949:   /*KSPSetOperators(ksp,A,A);*/
    950:   KSPSetDM(ksp,dmF);
    951:   KSPSetDMActive(ksp,PETSC_TRUE);
    952:   KSPSetFromOptions(ksp);

    954:   KSPSolve(ksp,b,x);

    956:   for (d=0; d<nd; d++) {
    957:     DM first = dms[d*nref+0];

    959:     if (first) {
    960:       UserContext *ctx = NULL;

    962:       DMGetApplicationContext(first,(void*)&ctx);
    963:       if (ctx) { PetscFree(ctx); }
    964:       DMSetApplicationContext(first,NULL);
    965:     }
    966:     for (k=1; k<nref; k++) {
    967:       DM dm = dms[d*nref+k];
    968:       if (dm) {
    969:         DMSetApplicationContext(dm,NULL);
    970:       }
    971:     }
    972:   }

    974:   for (k=0; k<nd*nref; k++) {
    975:     if (dms[k]) {
    976:       DMDestroyShellDMDA(&dms[k]);
    977:     }
    978:   }
    979:   PetscFree(dms);

    981:   KSPDestroy(&ksp);
    982:   MatDestroy(&A);
    983:   VecDestroy(&b);
    984:   VecDestroy(&x);

    986:   for (k=0; k<nd; k++) {
    987:     if (comms[k] != MPI_COMM_NULL) {
    988:       PetscCommDestroy(&comms[k]);
    989:     }
    990:   }
    991:   PetscFree(comms);
    992:   return(0);
    993: }

    995: int main(int argc,char **argv)
    996: {
    998:   PetscInt       test_id = 0;

    1000:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
    1001:   PetscOptionsGetInt(NULL,NULL,"-tid",&test_id,NULL);
    1002:   switch (test_id) {
    1003:   case 0:
    1004:     test_basic();
    1005:       break;
    1006:   case 1:
    1007:     test_hierarchy();
    1008:       break;
    1009:   case 2:
    1010:     test_mg();
    1011:       break;
    1012:   default:
    1013:     SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"-tid must be 0,1,2");
    1014:       break;
    1015:   }
    1016:   PetscFinalize();
    1017:   return ierr;
    1018: }

    1020: PetscErrorCode ComputeRHS_DMDA(DM da,Vec b,void *ctx)
    1021: {
    1022:   UserContext    *user = (UserContext*)ctx;
    1024:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
    1025:   PetscScalar    Hx,Hy;
    1026:   PetscScalar    **array;
    1027:   PetscBool      isda = PETSC_FALSE;

    1030:   PetscObjectTypeCompare((PetscObject)da,DMDA,&isda);
    1031:   if (!isda) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_USER,"DM provided must be a DMDA");
    1032:   DMDAGetInfo(da,NULL,&mx,&my,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
    1033:   Hx   = 1.0 / (PetscReal)(mx-1);
    1034:   Hy   = 1.0 / (PetscReal)(my-1);
    1035:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
    1036:   DMDAVecGetArray(da,b,&array);
    1037:   for (j=ys; j<ys+ym; j++) {
    1038:     for (i=xs; i<xs+xm; i++) {
    1039:       array[j][i] = PetscExpScalar(-((PetscReal)i*Hx)*((PetscReal)i*Hx)/user->nu)*PetscExpScalar(-((PetscReal)j*Hy)*((PetscReal)j*Hy)/user->nu)*Hx*Hy;
    1040:     }
    1041:   }
    1042:   DMDAVecRestoreArray(da, b, &array);
    1043:   VecAssemblyBegin(b);
    1044:   VecAssemblyEnd(b);

    1046:   /* force right hand side to be consistent for singular matrix */
    1047:   /* note this is really a hack, normally the model would provide you with a consistent right handside */
    1048:   if (user->bcType == NEUMANN) {
    1049:     MatNullSpace nullspace;

    1051:     MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);
    1052:     MatNullSpaceRemove(nullspace,b);
    1053:     MatNullSpaceDestroy(&nullspace);
    1054:   }
    1055:   return(0);
    1056: }

    1058: PetscErrorCode ComputeRho(PetscInt i, PetscInt j, PetscInt mx, PetscInt my, PetscReal centerRho, PetscReal *rho)
    1059: {
    1061:   if ((i > mx/3.0) && (i < 2.0*mx/3.0) && (j > my/3.0) && (j < 2.0*my/3.0)) {
    1062:     *rho = centerRho;
    1063:   } else {
    1064:     *rho = 1.0;
    1065:   }
    1066:   return(0);
    1067: }

    1069: PetscErrorCode ComputeMatrix_DMDA(DM da,Mat J,Mat jac,void *ctx)
    1070: {
    1071:   UserContext    *user = (UserContext*)ctx;
    1072:   PetscReal      centerRho;
    1074:   PetscInt       i,j,mx,my,xm,ym,xs,ys;
    1075:   PetscScalar    v[5];
    1076:   PetscReal      Hx,Hy,HydHx,HxdHy,rho;
    1077:   MatStencil     row, col[5];
    1078:   PetscBool      isda = PETSC_FALSE;

    1081:   PetscObjectTypeCompare((PetscObject)da,DMDA,&isda);
    1082:   if (!isda) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_USER,"DM provided must be a DMDA");
    1083:   MatZeroEntries(jac);
    1084:   centerRho = user->rho;
    1085:   DMDAGetInfo(da,NULL,&mx,&my,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
    1086:   Hx        = 1.0 / (PetscReal)(mx-1);
    1087:   Hy        = 1.0 / (PetscReal)(my-1);
    1088:   HxdHy     = Hx/Hy;
    1089:   HydHx     = Hy/Hx;
    1090:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
    1091:   for (j=ys; j<ys+ym; j++) {
    1092:     for (i=xs; i<xs+xm; i++) {
    1093:       row.i = i; row.j = j;
    1094:       ComputeRho(i, j, mx, my, centerRho, &rho);
    1095:       if (i==0 || j==0 || i==mx-1 || j==my-1) {
    1096:         if (user->bcType == DIRICHLET) {
    1097:           v[0] = 2.0*rho*(HxdHy + HydHx);
    1098:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
    1099:         } else if (user->bcType == NEUMANN) {
    1100:           PetscInt numx = 0, numy = 0, num = 0;
    1101:           if (j!=0) {
    1102:             v[num] = -rho*HxdHy;  col[num].i = i;    col[num].j = j-1;
    1103:             numy++; num++;
    1104:           }
    1105:           if (i!=0) {
    1106:             v[num] = -rho*HydHx;  col[num].i = i-1;  col[num].j = j;
    1107:             numx++; num++;
    1108:           }
    1109:           if (i!=mx-1) {
    1110:             v[num] = -rho*HydHx;  col[num].i = i+1;  col[num].j = j;
    1111:             numx++; num++;
    1112:           }
    1113:           if (j!=my-1) {
    1114:             v[num] = -rho*HxdHy;  col[num].i = i;    col[num].j = j+1;
    1115:             numy++; num++;
    1116:           }
    1117:           v[num] = numx*rho*HydHx + numy*rho*HxdHy;  col[num].i = i; col[num].j = j;
    1118:           num++;
    1119:           MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);
    1120:         }
    1121:       } else {
    1122:         v[0] = -rho*HxdHy;              col[0].i = i;   col[0].j = j-1;
    1123:         v[1] = -rho*HydHx;              col[1].i = i-1; col[1].j = j;
    1124:         v[2] = 2.0*rho*(HxdHy + HydHx); col[2].i = i;   col[2].j = j;
    1125:         v[3] = -rho*HydHx;              col[3].i = i+1; col[3].j = j;
    1126:         v[4] = -rho*HxdHy;              col[4].i = i;   col[4].j = j+1;
    1127:         MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);
    1128:       }
    1129:     }
    1130:   }
    1131:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    1132:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    1133:   return(0);
    1134: }

    1136: PetscErrorCode ComputeMatrix_ShellDA(KSP ksp,Mat J,Mat jac,void *ctx)
    1137: {
    1139:   DM             dm,da;
    1141:   KSPGetDM(ksp,&dm);
    1142:   DMShellGetContext(dm,(void**)&da);
    1143:   ComputeMatrix_DMDA(da,J,jac,ctx);
    1144:   return(0);
    1145: }

    1147: /*TEST
    1148:
    1149:   test:
    1150:     suffix: basic_dirichlet
    1151:     nsize: 4
    1152:     args: -tid 0 -ksp_monitor_short -pc_type telescope -telescope_ksp_max_it 100000 -telescope_pc_type lu -telescope_ksp_type fgmres -telescope_ksp_monitor_short -ksp_type gcr

    1154:   test:
    1155:     suffix: basic_neumann
    1156:     nsize: 4
    1157:     requires: !single
    1158:     args: -tid 0 -ksp_monitor_short -pc_type telescope -telescope_ksp_max_it 100000 -telescope_pc_type jacobi -telescope_ksp_type fgmres -telescope_ksp_monitor_short -ksp_type gcr -bc_type neumann

    1160:   test:
    1161:     suffix: mg_2lv_2mg
    1162:     nsize: 6
    1163:     args: -tid 2 -ksp_monitor_short -ksp_type gcr -pc_type mg -pc_mg_levels 3 -level_nrefs 3 -ndecomps 2 -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_use_coarse_dm -mg_coarse_telescope_pc_type mg -mg_coarse_telescope_pc_mg_levels 3 -level_comm_red_factor 6 -mg_coarse_telescope_mg_coarse_pc_type lu

    1165:   test:
    1166:     suffix: mg_3lv_2mg
    1167:     nsize: 4
    1168:     args: -tid 2 -ksp_monitor_short -ksp_type gcr -pc_type mg -pc_mg_levels 3 -level_nrefs 3 -ndecomps 3 -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_use_coarse_dm -mg_coarse_telescope_pc_type mg -mg_coarse_telescope_pc_mg_levels 3 -mg_coarse_telescope_mg_coarse_pc_type telescope -mg_coarse_telescope_mg_coarse_pc_telescope_use_coarse_dm -mg_coarse_telescope_mg_coarse_telescope_pc_type lu -m 5

    1170:   test:
    1171:     suffix: mg_3lv_2mg_customcommsize
    1172:     nsize: 12
    1173:     args: -tid 2 -ksp_monitor_short -ksp_type gcr -pc_type mg -pc_mg_levels 3 -level_nrefs 3 -ndecomps 3 -mg_coarse_pc_type telescope -mg_coarse_pc_telescope_use_coarse_dm  -m 5 -level_comm_red_factor 2,6 -mg_coarse_telescope_pc_type mg -mg_coarse_telescope_pc_mg_levels 3 -mg_coarse_telescope_mg_coarse_pc_type telescope -mg_coarse_telescope_mg_coarse_pc_telescope_use_coarse_dm -mg_coarse_telescope_mg_coarse_telescope_pc_type lu

    1175:  TEST*/