Date: 2022-03-31T04:47:28+00:00

Actual source code: dainterp.c

      2: /*
      3:   Code for interpolating between grids represented by DMDAs
      4: */

      6: /*
      7:       For linear elements there are two branches of code to compute the interpolation. They should compute the same results but may not. The "new version" does
      8:    not work for periodic domains, the old does. Change NEWVERSION to 1 to compile in the new version. Eventually when we are sure the two produce identical results
      9:    we will remove/merge the new version. Based on current tests, these both produce the same results. We are leaving NEWVERSION for now in the code since some
     10:    consider it cleaner, but old version is turned on since it handles periodic case.
     11: */
     12: #define NEWVERSION 0

     14: #include <petsc/private/dmdaimpl.h>

     16: /*
     17:    Since the interpolation uses MATMAIJ for dof > 0 we convert request for non-MATAIJ baseded matrices to MATAIJ.
     18:    This is a bit of a hack, the reason for it is partially because -dm_mat_type defines the
     19:    matrix type for both the operator matrices and the interpolation matrices so that users
     20:    can select matrix types of base MATAIJ for accelerators
     21: */
     22: static PetscErrorCode ConvertToAIJ(MatType intype,MatType *outtype)
     23: {
     24:   PetscInt       i;
     25:   char           const *types[3] = {MATAIJ,MATSEQAIJ,MATMPIAIJ};
     26:   PetscBool      flg;

     28:   *outtype = MATAIJ;
     29:   for (i=0; i<3; i++) {
     30:     PetscStrbeginswith(intype,types[i],&flg);
     31:     if (flg) {
     32:       *outtype = intype;
     33:       return 0;
     34:     }
     35:   }
     36:   return 0;
     37: }

     39: PetscErrorCode DMCreateInterpolation_DA_1D_Q1(DM dac,DM daf,Mat *A)
     40: {
     41:   PetscInt               i,i_start,m_f,Mx;
     42:   const PetscInt         *idx_f,*idx_c;
     43:   PetscInt               m_ghost,m_ghost_c;
     44:   PetscInt               row,col,i_start_ghost,mx,m_c,nc,ratio;
     45:   PetscInt               i_c,i_start_c,i_start_ghost_c,cols[2],dof;
     46:   PetscScalar            v[2],x;
     47:   Mat                    mat;
     48:   DMBoundaryType         bx;
     49:   ISLocalToGlobalMapping ltog_f,ltog_c;
     50:   MatType                mattype;

     52:   DMDAGetInfo(dac,NULL,&Mx,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&bx,NULL,NULL,NULL);
     53:   DMDAGetInfo(daf,NULL,&mx,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
     54:   if (bx == DM_BOUNDARY_PERIODIC) {
     55:     ratio = mx/Mx;
     57:   } else {
     58:     ratio = (mx-1)/(Mx-1);
     60:   }

     62:   DMDAGetCorners(daf,&i_start,NULL,NULL,&m_f,NULL,NULL);
     63:   DMDAGetGhostCorners(daf,&i_start_ghost,NULL,NULL,&m_ghost,NULL,NULL);
     64:   DMGetLocalToGlobalMapping(daf,&ltog_f);
     65:   ISLocalToGlobalMappingGetBlockIndices(ltog_f,&idx_f);

     67:   DMDAGetCorners(dac,&i_start_c,NULL,NULL,&m_c,NULL,NULL);
     68:   DMDAGetGhostCorners(dac,&i_start_ghost_c,NULL,NULL,&m_ghost_c,NULL,NULL);
     69:   DMGetLocalToGlobalMapping(dac,&ltog_c);
     70:   ISLocalToGlobalMappingGetBlockIndices(ltog_c,&idx_c);

     72:   /* create interpolation matrix */
     73:   MatCreate(PetscObjectComm((PetscObject)dac),&mat);
     74: #if defined(PETSC_HAVE_CUDA)
     75:   /*
     76:      Temporary hack: Since the MAIJ matrix must be converted to AIJ before being used by the GPU
     77:      we don't want the original unconverted matrix copied to the GPU
     78:    */
     79:   if (dof > 1) {
     80:     MatBindToCPU(mat,PETSC_TRUE);
     81:   }
     82:   #endif
     83:   MatSetSizes(mat,m_f,m_c,mx,Mx);
     84:   ConvertToAIJ(dac->mattype,&mattype);
     85:   MatSetType(mat,mattype);
     86:   MatSeqAIJSetPreallocation(mat,2,NULL);
     87:   MatMPIAIJSetPreallocation(mat,2,NULL,1,NULL);

     89:   /* loop over local fine grid nodes setting interpolation for those*/
     90:   if (!NEWVERSION) {

     92:     for (i=i_start; i<i_start+m_f; i++) {
     93:       /* convert to local "natural" numbering and then to PETSc global numbering */
     94:       row = idx_f[i-i_start_ghost];

     96:       i_c = (i/ratio);    /* coarse grid node to left of fine grid node */
     98:                                           i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);

    100:       /*
    101:        Only include those interpolation points that are truly
    102:        nonzero. Note this is very important for final grid lines
    103:        in x direction; since they have no right neighbor
    104:        */
    105:       x  = ((PetscReal)(i - i_c*ratio))/((PetscReal)ratio);
    106:       nc = 0;
    107:       /* one left and below; or we are right on it */
    108:       col      = (i_c-i_start_ghost_c);
    109:       cols[nc] = idx_c[col];
    110:       v[nc++]  = -x + 1.0;
    111:       /* one right? */
    112:       if (i_c*ratio != i) {
    113:         cols[nc] = idx_c[col+1];
    114:         v[nc++]  = x;
    115:       }
    116:       MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);
    117:     }

    119:   } else {
    120:     PetscScalar *xi;
    121:     PetscInt    li,nxi,n;
    122:     PetscScalar Ni[2];

    124:     /* compute local coordinate arrays */
    125:     nxi  = ratio + 1;
    126:     PetscMalloc1(nxi,&xi);
    127:     for (li=0; li<nxi; li++) {
    128:       xi[li] = -1.0 + (PetscScalar)li*(2.0/(PetscScalar)(nxi-1));
    129:     }

    131:     for (i=i_start; i<i_start+m_f; i++) {
    132:       /* convert to local "natural" numbering and then to PETSc global numbering */
    133:       row = idx_f[(i-i_start_ghost)];

    135:       i_c = (i/ratio);    /* coarse grid node to left of fine grid node */
    137:                                           i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);

    139:       /* remainders */
    140:       li = i - ratio * (i/ratio);
    141:       if (i==mx-1) li = nxi-1;

    143:       /* corners */
    144:       col     = (i_c-i_start_ghost_c);
    145:       cols[0] = idx_c[col];
    146:       Ni[0]   = 1.0;
    147:       if ((li==0) || (li==nxi-1)) {
    148:         MatSetValue(mat,row,cols[0],Ni[0],INSERT_VALUES);
    149:         continue;
    150:       }

    152:       /* edges + interior */
    153:       /* remainders */
    154:       if (i==mx-1) i_c--;

    156:       col     = (i_c-i_start_ghost_c);
    157:       cols[0] = idx_c[col]; /* one left and below; or we are right on it */
    158:       cols[1] = idx_c[col+1];

    160:       Ni[0] = 0.5*(1.0-xi[li]);
    161:       Ni[1] = 0.5*(1.0+xi[li]);
    162:       for (n=0; n<2; n++) {
    163:         if (PetscAbsScalar(Ni[n])<1.0e-32) cols[n]=-1;
    164:       }
    165:       MatSetValues(mat,1,&row,2,cols,Ni,INSERT_VALUES);
    166:     }
    167:     PetscFree(xi);
    168:   }
    169:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_f,&idx_f);
    170:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_c,&idx_c);
    171:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
    172:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);
    173:   MatCreateMAIJ(mat,dof,A);
    174:   MatDestroy(&mat);
    175:   return 0;
    176: }

    178: PetscErrorCode DMCreateInterpolation_DA_1D_Q0(DM dac,DM daf,Mat *A)
    179: {
    180:   PetscInt               i,i_start,m_f,Mx;
    181:   const PetscInt         *idx_f,*idx_c;
    182:   ISLocalToGlobalMapping ltog_f,ltog_c;
    183:   PetscInt               m_ghost,m_ghost_c;
    184:   PetscInt               row,col,i_start_ghost,mx,m_c,nc,ratio;
    185:   PetscInt               i_c,i_start_c,i_start_ghost_c,cols[2],dof;
    186:   PetscScalar            v[2],x;
    187:   Mat                    mat;
    188:   DMBoundaryType         bx;
    189:   MatType                mattype;

    191:   DMDAGetInfo(dac,NULL,&Mx,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&bx,NULL,NULL,NULL);
    192:   DMDAGetInfo(daf,NULL,&mx,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
    193:   if (bx == DM_BOUNDARY_PERIODIC) {
    195:     ratio = mx/Mx;
    197:   } else {
    199:     ratio = (mx-1)/(Mx-1);
    201:   }

    203:   DMDAGetCorners(daf,&i_start,NULL,NULL,&m_f,NULL,NULL);
    204:   DMDAGetGhostCorners(daf,&i_start_ghost,NULL,NULL,&m_ghost,NULL,NULL);
    205:   DMGetLocalToGlobalMapping(daf,&ltog_f);
    206:   ISLocalToGlobalMappingGetBlockIndices(ltog_f,&idx_f);

    208:   DMDAGetCorners(dac,&i_start_c,NULL,NULL,&m_c,NULL,NULL);
    209:   DMDAGetGhostCorners(dac,&i_start_ghost_c,NULL,NULL,&m_ghost_c,NULL,NULL);
    210:   DMGetLocalToGlobalMapping(dac,&ltog_c);
    211:   ISLocalToGlobalMappingGetBlockIndices(ltog_c,&idx_c);

    213:   /* create interpolation matrix */
    214:   MatCreate(PetscObjectComm((PetscObject)dac),&mat);
    215: #if defined(PETSC_HAVE_CUDA)
    216:   /*
    217:      Temporary hack: Since the MAIJ matrix must be converted to AIJ before being used by the GPU
    218:      we don't want the original unconverted matrix copied to the GPU
    219:    */
    220:   if (dof > 1) {
    221:     MatBindToCPU(mat,PETSC_TRUE);
    222:   }
    223:   #endif
    224:   MatSetSizes(mat,m_f,m_c,mx,Mx);
    225:   ConvertToAIJ(dac->mattype,&mattype);
    226:   MatSetType(mat,mattype);
    227:   MatSeqAIJSetPreallocation(mat,2,NULL);
    228:   MatMPIAIJSetPreallocation(mat,2,NULL,0,NULL);

    230:   /* loop over local fine grid nodes setting interpolation for those*/
    231:   for (i=i_start; i<i_start+m_f; i++) {
    232:     /* convert to local "natural" numbering and then to PETSc global numbering */
    233:     row = idx_f[(i-i_start_ghost)];

    235:     i_c = (i/ratio);    /* coarse grid node to left of fine grid node */

    237:     /*
    238:          Only include those interpolation points that are truly
    239:          nonzero. Note this is very important for final grid lines
    240:          in x direction; since they have no right neighbor
    241:     */
    242:     x  = ((PetscReal)(i - i_c*ratio))/((PetscReal)ratio);
    243:     nc = 0;
    244:     /* one left and below; or we are right on it */
    245:     col      = (i_c-i_start_ghost_c);
    246:     cols[nc] = idx_c[col];
    247:     v[nc++]  = -x + 1.0;
    248:     /* one right? */
    249:     if (i_c*ratio != i) {
    250:       cols[nc] = idx_c[col+1];
    251:       v[nc++]  = x;
    252:     }
    253:     MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);
    254:   }
    255:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_f,&idx_f);
    256:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_c,&idx_c);
    257:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
    258:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);
    259:   MatCreateMAIJ(mat,dof,A);
    260:   MatDestroy(&mat);
    261:   PetscLogFlops(5.0*m_f);
    262:   return 0;
    263: }

    265: PetscErrorCode DMCreateInterpolation_DA_2D_Q1(DM dac,DM daf,Mat *A)
    266: {
    267:   PetscErrorCode         ierr;
    268:   PetscInt               i,j,i_start,j_start,m_f,n_f,Mx,My,dof;
    269:   const PetscInt         *idx_c,*idx_f;
    270:   ISLocalToGlobalMapping ltog_f,ltog_c;
    271:   PetscInt               m_ghost,n_ghost,m_ghost_c,n_ghost_c,*dnz,*onz;
    272:   PetscInt               row,col,i_start_ghost,j_start_ghost,cols[4],mx,m_c,my,nc,ratioi,ratioj;
    273:   PetscInt               i_c,j_c,i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c,col_shift,col_scale;
    274:   PetscMPIInt            size_c,size_f,rank_f;
    275:   PetscScalar            v[4],x,y;
    276:   Mat                    mat;
    277:   DMBoundaryType         bx,by;
    278:   MatType                mattype;

    280:   DMDAGetInfo(dac,NULL,&Mx,&My,NULL,NULL,NULL,NULL,NULL,NULL,&bx,&by,NULL,NULL);
    281:   DMDAGetInfo(daf,NULL,&mx,&my,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
    282:   if (bx == DM_BOUNDARY_PERIODIC) {
    284:     ratioi = mx/Mx;
    286:   } else {
    288:     ratioi = (mx-1)/(Mx-1);
    290:   }
    291:   if (by == DM_BOUNDARY_PERIODIC) {
    293:     ratioj = my/My;
    295:   } else {
    297:     ratioj = (my-1)/(My-1);
    299:   }

    301:   DMDAGetCorners(daf,&i_start,&j_start,NULL,&m_f,&n_f,NULL);
    302:   DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,NULL,&m_ghost,&n_ghost,NULL);
    303:   DMGetLocalToGlobalMapping(daf,&ltog_f);
    304:   ISLocalToGlobalMappingGetBlockIndices(ltog_f,&idx_f);

    306:   DMDAGetCorners(dac,&i_start_c,&j_start_c,NULL,&m_c,&n_c,NULL);
    307:   DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,NULL,&m_ghost_c,&n_ghost_c,NULL);
    308:   DMGetLocalToGlobalMapping(dac,&ltog_c);
    309:   ISLocalToGlobalMappingGetBlockIndices(ltog_c,&idx_c);

    311:   /*
    312:    Used for handling a coarse DMDA that lives on 1/4 the processors of the fine DMDA.
    313:    The coarse vector is then duplicated 4 times (each time it lives on 1/4 of the
    314:    processors). It's effective length is hence 4 times its normal length, this is
    315:    why the col_scale is multiplied by the interpolation matrix column sizes.
    316:    sol_shift allows each set of 1/4 processors do its own interpolation using ITS
    317:    copy of the coarse vector. A bit of a hack but you do better.

    319:    In the standard case when size_f == size_c col_scale == 1 and col_shift == 0
    320:    */
    321:   MPI_Comm_size(PetscObjectComm((PetscObject)dac),&size_c);
    322:   MPI_Comm_size(PetscObjectComm((PetscObject)daf),&size_f);
    323:   MPI_Comm_rank(PetscObjectComm((PetscObject)daf),&rank_f);
    324:   col_scale = size_f/size_c;
    325:   col_shift = Mx*My*(rank_f/size_c);

    327:   MatPreallocateInitialize(PetscObjectComm((PetscObject)daf),m_f*n_f,col_scale*m_c*n_c,dnz,onz);
    328:   for (j=j_start; j<j_start+n_f; j++) {
    329:     for (i=i_start; i<i_start+m_f; i++) {
    330:       /* convert to local "natural" numbering and then to PETSc global numbering */
    331:       row = idx_f[(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];

    333:       i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
    334:       j_c = (j/ratioj);    /* coarse grid node below fine grid node */

    337:                                           j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
    339:                                           i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);

    341:       /*
    342:        Only include those interpolation points that are truly
    343:        nonzero. Note this is very important for final grid lines
    344:        in x and y directions; since they have no right/top neighbors
    345:        */
    346:       nc = 0;
    347:       /* one left and below; or we are right on it */
    348:       col        = (m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    349:       cols[nc++] = col_shift + idx_c[col];
    350:       /* one right and below */
    351:       if (i_c*ratioi != i) cols[nc++] = col_shift + idx_c[col+1];
    352:       /* one left and above */
    353:       if (j_c*ratioj != j) cols[nc++] = col_shift + idx_c[col+m_ghost_c];
    354:       /* one right and above */
    355:       if (i_c*ratioi != i && j_c*ratioj != j) cols[nc++] = col_shift + idx_c[col+(m_ghost_c+1)];
    356:       MatPreallocateSet(row,nc,cols,dnz,onz);
    357:     }
    358:   }
    359:   MatCreate(PetscObjectComm((PetscObject)daf),&mat);
    360: #if defined(PETSC_HAVE_CUDA)
    361:   /*
    362:      Temporary hack: Since the MAIJ matrix must be converted to AIJ before being used by the GPU
    363:      we don't want the original unconverted matrix copied to the GPU
    364:   */
    365:   if (dof > 1) {
    366:     MatBindToCPU(mat,PETSC_TRUE);
    367:   }
    368: #endif
    369:   MatSetSizes(mat,m_f*n_f,col_scale*m_c*n_c,mx*my,col_scale*Mx*My);
    370:   ConvertToAIJ(dac->mattype,&mattype);
    371:   MatSetType(mat,mattype);
    372:   MatSeqAIJSetPreallocation(mat,0,dnz);
    373:   MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);
    374:   MatPreallocateFinalize(dnz,onz);

    376:   /* loop over local fine grid nodes setting interpolation for those*/
    377:   if (!NEWVERSION) {

    379:     for (j=j_start; j<j_start+n_f; j++) {
    380:       for (i=i_start; i<i_start+m_f; i++) {
    381:         /* convert to local "natural" numbering and then to PETSc global numbering */
    382:         row = idx_f[(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];

    384:         i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
    385:         j_c = (j/ratioj);    /* coarse grid node below fine grid node */

    387:         /*
    388:          Only include those interpolation points that are truly
    389:          nonzero. Note this is very important for final grid lines
    390:          in x and y directions; since they have no right/top neighbors
    391:          */
    392:         x = ((PetscReal)(i - i_c*ratioi))/((PetscReal)ratioi);
    393:         y = ((PetscReal)(j - j_c*ratioj))/((PetscReal)ratioj);

    395:         nc = 0;
    396:         /* one left and below; or we are right on it */
    397:         col      = (m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    398:         cols[nc] = col_shift + idx_c[col];
    399:         v[nc++]  = x*y - x - y + 1.0;
    400:         /* one right and below */
    401:         if (i_c*ratioi != i) {
    402:           cols[nc] = col_shift + idx_c[col+1];
    403:           v[nc++]  = -x*y + x;
    404:         }
    405:         /* one left and above */
    406:         if (j_c*ratioj != j) {
    407:           cols[nc] = col_shift + idx_c[col+m_ghost_c];
    408:           v[nc++]  = -x*y + y;
    409:         }
    410:         /* one right and above */
    411:         if (j_c*ratioj != j && i_c*ratioi != i) {
    412:           cols[nc] = col_shift + idx_c[col+(m_ghost_c+1)];
    413:           v[nc++]  = x*y;
    414:         }
    415:         MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);
    416:       }
    417:     }

    419:   } else {
    420:     PetscScalar Ni[4];
    421:     PetscScalar *xi,*eta;
    422:     PetscInt    li,nxi,lj,neta;

    424:     /* compute local coordinate arrays */
    425:     nxi  = ratioi + 1;
    426:     neta = ratioj + 1;
    427:     PetscMalloc1(nxi,&xi);
    428:     PetscMalloc1(neta,&eta);
    429:     for (li=0; li<nxi; li++) {
    430:       xi[li] = -1.0 + (PetscScalar)li*(2.0/(PetscScalar)(nxi-1));
    431:     }
    432:     for (lj=0; lj<neta; lj++) {
    433:       eta[lj] = -1.0 + (PetscScalar)lj*(2.0/(PetscScalar)(neta-1));
    434:     }

    436:     /* loop over local fine grid nodes setting interpolation for those*/
    437:     for (j=j_start; j<j_start+n_f; j++) {
    438:       for (i=i_start; i<i_start+m_f; i++) {
    439:         /* convert to local "natural" numbering and then to PETSc global numbering */
    440:         row = idx_f[(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];

    442:         i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
    443:         j_c = (j/ratioj);    /* coarse grid node below fine grid node */

    445:         /* remainders */
    446:         li = i - ratioi * (i/ratioi);
    447:         if (i==mx-1) li = nxi-1;
    448:         lj = j - ratioj * (j/ratioj);
    449:         if (j==my-1) lj = neta-1;

    451:         /* corners */
    452:         col     = (m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    453:         cols[0] = col_shift + idx_c[col]; /* left, below */
    454:         Ni[0]   = 1.0;
    455:         if ((li==0) || (li==nxi-1)) {
    456:           if ((lj==0) || (lj==neta-1)) {
    457:             MatSetValue(mat,row,cols[0],Ni[0],INSERT_VALUES);
    458:             continue;
    459:           }
    460:         }

    462:         /* edges + interior */
    463:         /* remainders */
    464:         if (i==mx-1) i_c--;
    465:         if (j==my-1) j_c--;

    467:         col     = (m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    468:         cols[0] = col_shift + idx_c[col]; /* left, below */
    469:         cols[1] = col_shift + idx_c[col+1]; /* right, below */
    470:         cols[2] = col_shift + idx_c[col+m_ghost_c]; /* left, above */
    471:         cols[3] = col_shift + idx_c[col+(m_ghost_c+1)]; /* right, above */

    473:         Ni[0] = 0.25*(1.0-xi[li])*(1.0-eta[lj]);
    474:         Ni[1] = 0.25*(1.0+xi[li])*(1.0-eta[lj]);
    475:         Ni[2] = 0.25*(1.0-xi[li])*(1.0+eta[lj]);
    476:         Ni[3] = 0.25*(1.0+xi[li])*(1.0+eta[lj]);

    478:         nc = 0;
    479:         if (PetscAbsScalar(Ni[0])<1.0e-32) cols[0]=-1;
    480:         if (PetscAbsScalar(Ni[1])<1.0e-32) cols[1]=-1;
    481:         if (PetscAbsScalar(Ni[2])<1.0e-32) cols[2]=-1;
    482:         if (PetscAbsScalar(Ni[3])<1.0e-32) cols[3]=-1;

    484:         MatSetValues(mat,1,&row,4,cols,Ni,INSERT_VALUES);
    485:       }
    486:     }
    487:     PetscFree(xi);
    488:     PetscFree(eta);
    489:   }
    490:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_f,&idx_f);
    491:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_c,&idx_c);
    492:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
    493:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);
    494:   MatCreateMAIJ(mat,dof,A);
    495:   MatDestroy(&mat);
    496:   return 0;
    497: }

    499: /*
    500:        Contributed by Andrei Draganescu <aidraga@sandia.gov>
    501: */
    502: PetscErrorCode DMCreateInterpolation_DA_2D_Q0(DM dac,DM daf,Mat *A)
    503: {
    504:   PetscErrorCode         ierr;
    505:   PetscInt               i,j,i_start,j_start,m_f,n_f,Mx,My,dof;
    506:   const PetscInt         *idx_c,*idx_f;
    507:   ISLocalToGlobalMapping ltog_f,ltog_c;
    508:   PetscInt               m_ghost,n_ghost,m_ghost_c,n_ghost_c,*dnz,*onz;
    509:   PetscInt               row,col,i_start_ghost,j_start_ghost,cols[4],mx,m_c,my,nc,ratioi,ratioj;
    510:   PetscInt               i_c,j_c,i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c,col_shift,col_scale;
    511:   PetscMPIInt            size_c,size_f,rank_f;
    512:   PetscScalar            v[4];
    513:   Mat                    mat;
    514:   DMBoundaryType         bx,by;
    515:   MatType                mattype;

    517:   DMDAGetInfo(dac,NULL,&Mx,&My,NULL,NULL,NULL,NULL,NULL,NULL,&bx,&by,NULL,NULL);
    518:   DMDAGetInfo(daf,NULL,&mx,&my,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
    521:   ratioi = mx/Mx;
    522:   ratioj = my/My;

    528:   DMDAGetCorners(daf,&i_start,&j_start,NULL,&m_f,&n_f,NULL);
    529:   DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,NULL,&m_ghost,&n_ghost,NULL);
    530:   DMGetLocalToGlobalMapping(daf,&ltog_f);
    531:   ISLocalToGlobalMappingGetBlockIndices(ltog_f,&idx_f);

    533:   DMDAGetCorners(dac,&i_start_c,&j_start_c,NULL,&m_c,&n_c,NULL);
    534:   DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,NULL,&m_ghost_c,&n_ghost_c,NULL);
    535:   DMGetLocalToGlobalMapping(dac,&ltog_c);
    536:   ISLocalToGlobalMappingGetBlockIndices(ltog_c,&idx_c);

    538:   /*
    539:      Used for handling a coarse DMDA that lives on 1/4 the processors of the fine DMDA.
    540:      The coarse vector is then duplicated 4 times (each time it lives on 1/4 of the
    541:      processors). It's effective length is hence 4 times its normal length, this is
    542:      why the col_scale is multiplied by the interpolation matrix column sizes.
    543:      sol_shift allows each set of 1/4 processors do its own interpolation using ITS
    544:      copy of the coarse vector. A bit of a hack but you do better.

    546:      In the standard case when size_f == size_c col_scale == 1 and col_shift == 0
    547:   */
    548:   MPI_Comm_size(PetscObjectComm((PetscObject)dac),&size_c);
    549:   MPI_Comm_size(PetscObjectComm((PetscObject)daf),&size_f);
    550:   MPI_Comm_rank(PetscObjectComm((PetscObject)daf),&rank_f);
    551:   col_scale = size_f/size_c;
    552:   col_shift = Mx*My*(rank_f/size_c);

    554:   MatPreallocateInitialize(PetscObjectComm((PetscObject)daf),m_f*n_f,col_scale*m_c*n_c,dnz,onz);
    555:   for (j=j_start; j<j_start+n_f; j++) {
    556:     for (i=i_start; i<i_start+m_f; i++) {
    557:       /* convert to local "natural" numbering and then to PETSc global numbering */
    558:       row = idx_f[(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];

    560:       i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
    561:       j_c = (j/ratioj);    /* coarse grid node below fine grid node */

    564:     j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
    566:     i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);

    568:       /*
    569:          Only include those interpolation points that are truly
    570:          nonzero. Note this is very important for final grid lines
    571:          in x and y directions; since they have no right/top neighbors
    572:       */
    573:       nc = 0;
    574:       /* one left and below; or we are right on it */
    575:       col        = (m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    576:       cols[nc++] = col_shift + idx_c[col];
    577:       MatPreallocateSet(row,nc,cols,dnz,onz);
    578:     }
    579:   }
    580:   MatCreate(PetscObjectComm((PetscObject)daf),&mat);
    581: #if defined(PETSC_HAVE_CUDA)
    582:   /*
    583:      Temporary hack: Since the MAIJ matrix must be converted to AIJ before being used by the GPU
    584:      we don't want the original unconverted matrix copied to the GPU
    585:   */
    586:   if (dof > 1) {
    587:     MatBindToCPU(mat,PETSC_TRUE);
    588:   }
    589:   #endif
    590:   MatSetSizes(mat,m_f*n_f,col_scale*m_c*n_c,mx*my,col_scale*Mx*My);
    591:   ConvertToAIJ(dac->mattype,&mattype);
    592:   MatSetType(mat,mattype);
    593:   MatSeqAIJSetPreallocation(mat,0,dnz);
    594:   MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);
    595:   MatPreallocateFinalize(dnz,onz);

    597:   /* loop over local fine grid nodes setting interpolation for those*/
    598:   for (j=j_start; j<j_start+n_f; j++) {
    599:     for (i=i_start; i<i_start+m_f; i++) {
    600:       /* convert to local "natural" numbering and then to PETSc global numbering */
    601:       row = idx_f[(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];

    603:       i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
    604:       j_c = (j/ratioj);    /* coarse grid node below fine grid node */
    605:       nc  = 0;
    606:       /* one left and below; or we are right on it */
    607:       col      = (m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    608:       cols[nc] = col_shift + idx_c[col];
    609:       v[nc++]  = 1.0;

    611:       MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);
    612:     }
    613:   }
    614:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_f,&idx_f);
    615:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_c,&idx_c);
    616:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
    617:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);
    618:   MatCreateMAIJ(mat,dof,A);
    619:   MatDestroy(&mat);
    620:   PetscLogFlops(13.0*m_f*n_f);
    621:   return 0;
    622: }

    624: /*
    625:        Contributed by Jianming Yang <jianming-yang@uiowa.edu>
    626: */
    627: PetscErrorCode DMCreateInterpolation_DA_3D_Q0(DM dac,DM daf,Mat *A)
    628: {
    629:   PetscErrorCode         ierr;
    630:   PetscInt               i,j,l,i_start,j_start,l_start,m_f,n_f,p_f,Mx,My,Mz,dof;
    631:   const PetscInt         *idx_c,*idx_f;
    632:   ISLocalToGlobalMapping ltog_f,ltog_c;
    633:   PetscInt               m_ghost,n_ghost,p_ghost,m_ghost_c,n_ghost_c,p_ghost_c,nc,*dnz,*onz;
    634:   PetscInt               row,col,i_start_ghost,j_start_ghost,l_start_ghost,cols[8],mx,m_c,my,n_c,mz,p_c,ratioi,ratioj,ratiol;
    635:   PetscInt               i_c,j_c,l_c,i_start_c,j_start_c,l_start_c,i_start_ghost_c,j_start_ghost_c,l_start_ghost_c,col_shift,col_scale;
    636:   PetscMPIInt            size_c,size_f,rank_f;
    637:   PetscScalar            v[8];
    638:   Mat                    mat;
    639:   DMBoundaryType         bx,by,bz;
    640:   MatType                mattype;

    642:   DMDAGetInfo(dac,NULL,&Mx,&My,&Mz,NULL,NULL,NULL,NULL,NULL,&bx,&by,&bz,NULL);
    646:   DMDAGetInfo(daf,NULL,&mx,&my,&mz,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
    647:   ratioi = mx/Mx;
    648:   ratioj = my/My;
    649:   ratiol = mz/Mz;

    657:   DMDAGetCorners(daf,&i_start,&j_start,&l_start,&m_f,&n_f,&p_f);
    658:   DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&l_start_ghost,&m_ghost,&n_ghost,&p_ghost);
    659:   DMGetLocalToGlobalMapping(daf,&ltog_f);
    660:   ISLocalToGlobalMappingGetBlockIndices(ltog_f,&idx_f);

    662:   DMDAGetCorners(dac,&i_start_c,&j_start_c,&l_start_c,&m_c,&n_c,&p_c);
    663:   DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,&l_start_ghost_c,&m_ghost_c,&n_ghost_c,&p_ghost_c);
    664:   DMGetLocalToGlobalMapping(dac,&ltog_c);
    665:   ISLocalToGlobalMappingGetBlockIndices(ltog_c,&idx_c);

    667:   /*
    668:      Used for handling a coarse DMDA that lives on 1/4 the processors of the fine DMDA.
    669:      The coarse vector is then duplicated 4 times (each time it lives on 1/4 of the
    670:      processors). It's effective length is hence 4 times its normal length, this is
    671:      why the col_scale is multiplied by the interpolation matrix column sizes.
    672:      sol_shift allows each set of 1/4 processors do its own interpolation using ITS
    673:      copy of the coarse vector. A bit of a hack but you do better.

    675:      In the standard case when size_f == size_c col_scale == 1 and col_shift == 0
    676:   */
    677:   MPI_Comm_size(PetscObjectComm((PetscObject)dac),&size_c);
    678:   MPI_Comm_size(PetscObjectComm((PetscObject)daf),&size_f);
    679:   MPI_Comm_rank(PetscObjectComm((PetscObject)daf),&rank_f);
    680:   col_scale = size_f/size_c;
    681:   col_shift = Mx*My*Mz*(rank_f/size_c);

    683:   MatPreallocateInitialize(PetscObjectComm((PetscObject)daf),m_f*n_f*p_f,col_scale*m_c*n_c*p_c,dnz,onz);
    684:   for (l=l_start; l<l_start+p_f; l++) {
    685:     for (j=j_start; j<j_start+n_f; j++) {
    686:       for (i=i_start; i<i_start+m_f; i++) {
    687:         /* convert to local "natural" numbering and then to PETSc global numbering */
    688:         row = idx_f[(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];

    690:         i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
    691:         j_c = (j/ratioj);    /* coarse grid node below fine grid node */
    692:         l_c = (l/ratiol);

    695:     l_start %D l_c %D l_start_ghost_c %D",l_start,l_c,l_start_ghost_c);
    697:     j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
    699:     i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);

    701:         /*
    702:            Only include those interpolation points that are truly
    703:            nonzero. Note this is very important for final grid lines
    704:            in x and y directions; since they have no right/top neighbors
    705:         */
    706:         nc = 0;
    707:         /* one left and below; or we are right on it */
    708:         col        = (m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    709:         cols[nc++] = col_shift + idx_c[col];
    710:         MatPreallocateSet(row,nc,cols,dnz,onz);
    711:       }
    712:     }
    713:   }
    714:   MatCreate(PetscObjectComm((PetscObject)daf),&mat);
    715: #if defined(PETSC_HAVE_CUDA)
    716:   /*
    717:      Temporary hack: Since the MAIJ matrix must be converted to AIJ before being used by the GPU
    718:      we don't want the original unconverted matrix copied to the GPU
    719:   */
    720:   if (dof > 1) {
    721:     MatBindToCPU(mat,PETSC_TRUE);
    722:   }
    723:   #endif
    724:   MatSetSizes(mat,m_f*n_f*p_f,col_scale*m_c*n_c*p_c,mx*my*mz,col_scale*Mx*My*Mz);
    725:   ConvertToAIJ(dac->mattype,&mattype);
    726:   MatSetType(mat,mattype);
    727:   MatSeqAIJSetPreallocation(mat,0,dnz);
    728:   MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);
    729:   MatPreallocateFinalize(dnz,onz);

    731:   /* loop over local fine grid nodes setting interpolation for those*/
    732:   for (l=l_start; l<l_start+p_f; l++) {
    733:     for (j=j_start; j<j_start+n_f; j++) {
    734:       for (i=i_start; i<i_start+m_f; i++) {
    735:         /* convert to local "natural" numbering and then to PETSc global numbering */
    736:         row = idx_f[(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];

    738:         i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
    739:         j_c = (j/ratioj);    /* coarse grid node below fine grid node */
    740:         l_c = (l/ratiol);
    741:         nc  = 0;
    742:         /* one left and below; or we are right on it */
    743:         col      = (m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    744:         cols[nc] = col_shift + idx_c[col];
    745:         v[nc++]  = 1.0;

    747:         MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);
    748:       }
    749:     }
    750:   }
    751:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_f,&idx_f);
    752:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_c,&idx_c);
    753:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
    754:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);
    755:   MatCreateMAIJ(mat,dof,A);
    756:   MatDestroy(&mat);
    757:   PetscLogFlops(13.0*m_f*n_f*p_f);
    758:   return 0;
    759: }

    761: PetscErrorCode DMCreateInterpolation_DA_3D_Q1(DM dac,DM daf,Mat *A)
    762: {
    763:   PetscErrorCode         ierr;
    764:   PetscInt               i,j,i_start,j_start,m_f,n_f,Mx,My,dof,l;
    765:   const PetscInt         *idx_c,*idx_f;
    766:   ISLocalToGlobalMapping ltog_f,ltog_c;
    767:   PetscInt               m_ghost,n_ghost,m_ghost_c,n_ghost_c,Mz,mz;
    768:   PetscInt               row,col,i_start_ghost,j_start_ghost,cols[8],mx,m_c,my,nc,ratioi,ratioj,ratiok;
    769:   PetscInt               i_c,j_c,i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c;
    770:   PetscInt               l_start,p_f,l_start_ghost,p_ghost,l_start_c,p_c;
    771:   PetscInt               l_start_ghost_c,p_ghost_c,l_c,*dnz,*onz;
    772:   PetscScalar            v[8],x,y,z;
    773:   Mat                    mat;
    774:   DMBoundaryType         bx,by,bz;
    775:   MatType                mattype;

    777:   DMDAGetInfo(dac,NULL,&Mx,&My,&Mz,NULL,NULL,NULL,NULL,NULL,&bx,&by,&bz,NULL);
    778:   DMDAGetInfo(daf,NULL,&mx,&my,&mz,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
    779:   if (mx == Mx) {
    780:     ratioi = 1;
    781:   } else if (bx == DM_BOUNDARY_PERIODIC) {
    783:     ratioi = mx/Mx;
    785:   } else {
    787:     ratioi = (mx-1)/(Mx-1);
    789:   }
    790:   if (my == My) {
    791:     ratioj = 1;
    792:   } else if (by == DM_BOUNDARY_PERIODIC) {
    794:     ratioj = my/My;
    796:   } else {
    798:     ratioj = (my-1)/(My-1);
    800:   }
    801:   if (mz == Mz) {
    802:     ratiok = 1;
    803:   } else if (bz == DM_BOUNDARY_PERIODIC) {
    805:     ratiok = mz/Mz;
    807:   } else {
    809:     ratiok = (mz-1)/(Mz-1);
    811:   }

    813:   DMDAGetCorners(daf,&i_start,&j_start,&l_start,&m_f,&n_f,&p_f);
    814:   DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&l_start_ghost,&m_ghost,&n_ghost,&p_ghost);
    815:   DMGetLocalToGlobalMapping(daf,&ltog_f);
    816:   ISLocalToGlobalMappingGetBlockIndices(ltog_f,&idx_f);

    818:   DMDAGetCorners(dac,&i_start_c,&j_start_c,&l_start_c,&m_c,&n_c,&p_c);
    819:   DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,&l_start_ghost_c,&m_ghost_c,&n_ghost_c,&p_ghost_c);
    820:   DMGetLocalToGlobalMapping(dac,&ltog_c);
    821:   ISLocalToGlobalMappingGetBlockIndices(ltog_c,&idx_c);

    823:   /* create interpolation matrix, determining exact preallocation */
    824:   MatPreallocateInitialize(PetscObjectComm((PetscObject)dac),m_f*n_f*p_f,m_c*n_c*p_c,dnz,onz);
    825:   /* loop over local fine grid nodes counting interpolating points */
    826:   for (l=l_start; l<l_start+p_f; l++) {
    827:     for (j=j_start; j<j_start+n_f; j++) {
    828:       for (i=i_start; i<i_start+m_f; i++) {
    829:         /* convert to local "natural" numbering and then to PETSc global numbering */
    830:         row = idx_f[(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];
    831:         i_c = (i/ratioi);
    832:         j_c = (j/ratioj);
    833:         l_c = (l/ratiok);
    835:                                             l_start %D l_c %D l_start_ghost_c %D",l_start,l_c,l_start_ghost_c);
    837:                                             j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
    839:                                             i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);

    841:         /*
    842:          Only include those interpolation points that are truly
    843:          nonzero. Note this is very important for final grid lines
    844:          in x and y directions; since they have no right/top neighbors
    845:          */
    846:         nc         = 0;
    847:         col        = (m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    848:         cols[nc++] = idx_c[col];
    849:         if (i_c*ratioi != i) {
    850:           cols[nc++] = idx_c[col+1];
    851:         }
    852:         if (j_c*ratioj != j) {
    853:           cols[nc++] = idx_c[col+m_ghost_c];
    854:         }
    855:         if (l_c*ratiok != l) {
    856:           cols[nc++] = idx_c[col+m_ghost_c*n_ghost_c];
    857:         }
    858:         if (j_c*ratioj != j && i_c*ratioi != i) {
    859:           cols[nc++] = idx_c[col+(m_ghost_c+1)];
    860:         }
    861:         if (j_c*ratioj != j && l_c*ratiok != l) {
    862:           cols[nc++] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c)];
    863:         }
    864:         if (i_c*ratioi != i && l_c*ratiok != l) {
    865:           cols[nc++] = idx_c[col+(m_ghost_c*n_ghost_c+1)];
    866:         }
    867:         if (i_c*ratioi != i && l_c*ratiok != l && j_c*ratioj != j) {
    868:           cols[nc++] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c+1)];
    869:         }
    870:         MatPreallocateSet(row,nc,cols,dnz,onz);
    871:       }
    872:     }
    873:   }
    874:   MatCreate(PetscObjectComm((PetscObject)dac),&mat);
    875: #if defined(PETSC_HAVE_CUDA)
    876:   /*
    877:      Temporary hack: Since the MAIJ matrix must be converted to AIJ before being used by the GPU
    878:      we don't want the original unconverted matrix copied to the GPU
    879:   */
    880:   if (dof > 1) {
    881:     MatBindToCPU(mat,PETSC_TRUE);
    882:   }
    883:   #endif
    884:   MatSetSizes(mat,m_f*n_f*p_f,m_c*n_c*p_c,mx*my*mz,Mx*My*Mz);
    885:   ConvertToAIJ(dac->mattype,&mattype);
    886:   MatSetType(mat,mattype);
    887:   MatSeqAIJSetPreallocation(mat,0,dnz);
    888:   MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);
    889:   MatPreallocateFinalize(dnz,onz);

    891:   /* loop over local fine grid nodes setting interpolation for those*/
    892:   if (!NEWVERSION) {

    894:     for (l=l_start; l<l_start+p_f; l++) {
    895:       for (j=j_start; j<j_start+n_f; j++) {
    896:         for (i=i_start; i<i_start+m_f; i++) {
    897:           /* convert to local "natural" numbering and then to PETSc global numbering */
    898:           row = idx_f[(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];

    900:           i_c = (i/ratioi);
    901:           j_c = (j/ratioj);
    902:           l_c = (l/ratiok);

    904:           /*
    905:            Only include those interpolation points that are truly
    906:            nonzero. Note this is very important for final grid lines
    907:            in x and y directions; since they have no right/top neighbors
    908:            */
    909:           x = ((PetscReal)(i - i_c*ratioi))/((PetscReal)ratioi);
    910:           y = ((PetscReal)(j - j_c*ratioj))/((PetscReal)ratioj);
    911:           z = ((PetscReal)(l - l_c*ratiok))/((PetscReal)ratiok);

    913:           nc = 0;
    914:           /* one left and below; or we are right on it */
    915:           col = (m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c)+m_ghost_c*(j_c-j_start_ghost_c)+(i_c-i_start_ghost_c));

    917:           cols[nc] = idx_c[col];
    918:           v[nc++]  = .125*(1. - (2.0*x-1.))*(1. - (2.0*y-1.))*(1. - (2.0*z-1.));

    920:           if (i_c*ratioi != i) {
    921:             cols[nc] = idx_c[col+1];
    922:             v[nc++]  = .125*(1. + (2.0*x-1.))*(1. - (2.0*y-1.))*(1. - (2.0*z-1.));
    923:           }

    925:           if (j_c*ratioj != j) {
    926:             cols[nc] = idx_c[col+m_ghost_c];
    927:             v[nc++]  = .125*(1. - (2.0*x-1.))*(1. + (2.0*y-1.))*(1. - (2.0*z-1.));
    928:           }

    930:           if (l_c*ratiok != l) {
    931:             cols[nc] = idx_c[col+m_ghost_c*n_ghost_c];
    932:             v[nc++]  = .125*(1. - (2.0*x-1.))*(1. - (2.0*y-1.))*(1. + (2.0*z-1.));
    933:           }

    935:           if (j_c*ratioj != j && i_c*ratioi != i) {
    936:             cols[nc] = idx_c[col+(m_ghost_c+1)];
    937:             v[nc++]  = .125*(1. + (2.0*x-1.))*(1. + (2.0*y-1.))*(1. - (2.0*z-1.));
    938:           }

    940:           if (j_c*ratioj != j && l_c*ratiok != l) {
    941:             cols[nc] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c)];
    942:             v[nc++]  = .125*(1. - (2.0*x-1.))*(1. + (2.0*y-1.))*(1. + (2.0*z-1.));
    943:           }

    945:           if (i_c*ratioi != i && l_c*ratiok != l) {
    946:             cols[nc] = idx_c[col+(m_ghost_c*n_ghost_c+1)];
    947:             v[nc++]  = .125*(1. + (2.0*x-1.))*(1. - (2.0*y-1.))*(1. + (2.0*z-1.));
    948:           }

    950:           if (i_c*ratioi != i && l_c*ratiok != l && j_c*ratioj != j) {
    951:             cols[nc] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c+1)];
    952:             v[nc++]  = .125*(1. + (2.0*x-1.))*(1. + (2.0*y-1.))*(1. + (2.0*z-1.));
    953:           }
    954:           MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);
    955:         }
    956:       }
    957:     }

    959:   } else {
    960:     PetscScalar *xi,*eta,*zeta;
    961:     PetscInt    li,nxi,lj,neta,lk,nzeta,n;
    962:     PetscScalar Ni[8];

    964:     /* compute local coordinate arrays */
    965:     nxi   = ratioi + 1;
    966:     neta  = ratioj + 1;
    967:     nzeta = ratiok + 1;
    968:     PetscMalloc1(nxi,&xi);
    969:     PetscMalloc1(neta,&eta);
    970:     PetscMalloc1(nzeta,&zeta);
    971:     for (li=0; li<nxi; li++) xi[li] = -1.0 + (PetscScalar)li*(2.0/(PetscScalar)(nxi-1));
    972:     for (lj=0; lj<neta; lj++) eta[lj] = -1.0 + (PetscScalar)lj*(2.0/(PetscScalar)(neta-1));
    973:     for (lk=0; lk<nzeta; lk++) zeta[lk] = -1.0 + (PetscScalar)lk*(2.0/(PetscScalar)(nzeta-1));

    975:     for (l=l_start; l<l_start+p_f; l++) {
    976:       for (j=j_start; j<j_start+n_f; j++) {
    977:         for (i=i_start; i<i_start+m_f; i++) {
    978:           /* convert to local "natural" numbering and then to PETSc global numbering */
    979:           row = idx_f[(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))];

    981:           i_c = (i/ratioi);
    982:           j_c = (j/ratioj);
    983:           l_c = (l/ratiok);

    985:           /* remainders */
    986:           li = i - ratioi * (i/ratioi);
    987:           if (i==mx-1) li = nxi-1;
    988:           lj = j - ratioj * (j/ratioj);
    989:           if (j==my-1) lj = neta-1;
    990:           lk = l - ratiok * (l/ratiok);
    991:           if (l==mz-1) lk = nzeta-1;

    993:           /* corners */
    994:           col     = (m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c)+m_ghost_c*(j_c-j_start_ghost_c)+(i_c-i_start_ghost_c));
    995:           cols[0] = idx_c[col];
    996:           Ni[0]   = 1.0;
    997:           if ((li==0) || (li==nxi-1)) {
    998:             if ((lj==0) || (lj==neta-1)) {
    999:               if ((lk==0) || (lk==nzeta-1)) {
    1000:                 MatSetValue(mat,row,cols[0],Ni[0],INSERT_VALUES);
    1001:                 continue;
    1002:               }
    1003:             }
    1004:           }

    1006:           /* edges + interior */
    1007:           /* remainders */
    1008:           if (i==mx-1) i_c--;
    1009:           if (j==my-1) j_c--;
    1010:           if (l==mz-1) l_c--;

    1012:           col     = (m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
    1013:           cols[0] = idx_c[col]; /* one left and below; or we are right on it */
    1014:           cols[1] = idx_c[col+1]; /* one right and below */
    1015:           cols[2] = idx_c[col+m_ghost_c];  /* one left and above */
    1016:           cols[3] = idx_c[col+(m_ghost_c+1)]; /* one right and above */

    1018:           cols[4] = idx_c[col+m_ghost_c*n_ghost_c]; /* one left and below and front; or we are right on it */
    1019:           cols[5] = idx_c[col+(m_ghost_c*n_ghost_c+1)]; /* one right and below, and front */
    1020:           cols[6] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c)]; /* one left and above and front*/
    1021:           cols[7] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c+1)]; /* one right and above and front */

    1023:           Ni[0] = 0.125*(1.0-xi[li])*(1.0-eta[lj])*(1.0-zeta[lk]);
    1024:           Ni[1] = 0.125*(1.0+xi[li])*(1.0-eta[lj])*(1.0-zeta[lk]);
    1025:           Ni[2] = 0.125*(1.0-xi[li])*(1.0+eta[lj])*(1.0-zeta[lk]);
    1026:           Ni[3] = 0.125*(1.0+xi[li])*(1.0+eta[lj])*(1.0-zeta[lk]);

    1028:           Ni[4] = 0.125*(1.0-xi[li])*(1.0-eta[lj])*(1.0+zeta[lk]);
    1029:           Ni[5] = 0.125*(1.0+xi[li])*(1.0-eta[lj])*(1.0+zeta[lk]);
    1030:           Ni[6] = 0.125*(1.0-xi[li])*(1.0+eta[lj])*(1.0+zeta[lk]);
    1031:           Ni[7] = 0.125*(1.0+xi[li])*(1.0+eta[lj])*(1.0+zeta[lk]);

    1033:           for (n=0; n<8; n++) {
    1034:             if (PetscAbsScalar(Ni[n])<1.0e-32) cols[n]=-1;
    1035:           }
    1036:           MatSetValues(mat,1,&row,8,cols,Ni,INSERT_VALUES);

    1038:         }
    1039:       }
    1040:     }
    1041:     PetscFree(xi);
    1042:     PetscFree(eta);
    1043:     PetscFree(zeta);
    1044:   }
    1045:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_f,&idx_f);
    1046:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_c,&idx_c);
    1047:   MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);
    1048:   MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);

    1050:   MatCreateMAIJ(mat,dof,A);
    1051:   MatDestroy(&mat);
    1052:   return 0;
    1053: }

    1055: PetscErrorCode  DMCreateInterpolation_DA(DM dac,DM daf,Mat *A,Vec *scale)
    1056: {
    1057:   PetscInt         dimc,Mc,Nc,Pc,mc,nc,pc,dofc,sc,dimf,Mf,Nf,Pf,mf,nf,pf,doff,sf;
    1058:   DMBoundaryType   bxc,byc,bzc,bxf,byf,bzf;
    1059:   DMDAStencilType  stc,stf;
    1060:   DM_DA            *ddc = (DM_DA*)dac->data;

    1067:   DMDAGetInfo(dac,&dimc,&Mc,&Nc,&Pc,&mc,&nc,&pc,&dofc,&sc,&bxc,&byc,&bzc,&stc);
    1068:   DMDAGetInfo(daf,&dimf,&Mf,&Nf,&Pf,&mf,&nf,&pf,&doff,&sf,&bxf,&byf,&bzf,&stf);

    1078:   if (ddc->interptype == DMDA_Q1) {
    1079:     if (dimc == 1) {
    1080:       DMCreateInterpolation_DA_1D_Q1(dac,daf,A);
    1081:     } else if (dimc == 2) {
    1082:       DMCreateInterpolation_DA_2D_Q1(dac,daf,A);
    1083:     } else if (dimc == 3) {
    1084:       DMCreateInterpolation_DA_3D_Q1(dac,daf,A);
    1085:     } else SETERRQ(PetscObjectComm((PetscObject)daf),PETSC_ERR_SUP,"No support for this DMDA dimension %D for interpolation type %d",dimc,(int)ddc->interptype);
    1086:   } else if (ddc->interptype == DMDA_Q0) {
    1087:     if (dimc == 1) {
    1088:       DMCreateInterpolation_DA_1D_Q0(dac,daf,A);
    1089:     } else if (dimc == 2) {
    1090:       DMCreateInterpolation_DA_2D_Q0(dac,daf,A);
    1091:     } else if (dimc == 3) {
    1092:       DMCreateInterpolation_DA_3D_Q0(dac,daf,A);
    1093:     } else SETERRQ(PetscObjectComm((PetscObject)daf),PETSC_ERR_SUP,"No support for this DMDA dimension %D for interpolation type %d",dimc,(int)ddc->interptype);
    1094:   }
    1095:   if (scale) {
    1096:     DMCreateInterpolationScale((DM)dac,(DM)daf,*A,scale);
    1097:   }
    1098:   return 0;
    1099: }

    1101: PetscErrorCode DMCreateInjection_DA_1D(DM dac,DM daf,VecScatter *inject)
    1102: {
    1103:   PetscInt               i,i_start,m_f,Mx,dof;
    1104:   const PetscInt         *idx_f;
    1105:   ISLocalToGlobalMapping ltog_f;
    1106:   PetscInt               m_ghost,m_ghost_c;
    1107:   PetscInt               row,i_start_ghost,mx,m_c,nc,ratioi;
    1108:   PetscInt               i_start_c,i_start_ghost_c;
    1109:   PetscInt               *cols;
    1110:   DMBoundaryType         bx;
    1111:   Vec                    vecf,vecc;
    1112:   IS                     isf;

    1114:   DMDAGetInfo(dac,NULL,&Mx,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&bx,NULL,NULL,NULL);
    1115:   DMDAGetInfo(daf,NULL,&mx,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
    1116:   if (bx == DM_BOUNDARY_PERIODIC) {
    1117:     ratioi = mx/Mx;
    1119:   } else {
    1120:     ratioi = (mx-1)/(Mx-1);
    1122:   }

    1124:   DMDAGetCorners(daf,&i_start,NULL,NULL,&m_f,NULL,NULL);
    1125:   DMDAGetGhostCorners(daf,&i_start_ghost,NULL,NULL,&m_ghost,NULL,NULL);
    1126:   DMGetLocalToGlobalMapping(daf,&ltog_f);
    1127:   ISLocalToGlobalMappingGetBlockIndices(ltog_f,&idx_f);

    1129:   DMDAGetCorners(dac,&i_start_c,NULL,NULL,&m_c,NULL,NULL);
    1130:   DMDAGetGhostCorners(dac,&i_start_ghost_c,NULL,NULL,&m_ghost_c,NULL,NULL);

    1132:   /* loop over local fine grid nodes setting interpolation for those*/
    1133:   nc   = 0;
    1134:   PetscMalloc1(m_f,&cols);

    1136:   for (i=i_start_c; i<i_start_c+m_c; i++) {
    1137:     PetscInt i_f = i*ratioi;

    1141:     row        = idx_f[(i_f-i_start_ghost)];
    1142:     cols[nc++] = row;
    1143:   }

    1145:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_f,&idx_f);
    1146:   ISCreateBlock(PetscObjectComm((PetscObject)daf),dof,nc,cols,PETSC_OWN_POINTER,&isf);
    1147:   DMGetGlobalVector(dac,&vecc);
    1148:   DMGetGlobalVector(daf,&vecf);
    1149:   VecScatterCreate(vecf,isf,vecc,NULL,inject);
    1150:   DMRestoreGlobalVector(dac,&vecc);
    1151:   DMRestoreGlobalVector(daf,&vecf);
    1152:   ISDestroy(&isf);
    1153:   return 0;
    1154: }

    1156: PetscErrorCode DMCreateInjection_DA_2D(DM dac,DM daf,VecScatter *inject)
    1157: {
    1158:   PetscInt               i,j,i_start,j_start,m_f,n_f,Mx,My,dof;
    1159:   const PetscInt         *idx_c,*idx_f;
    1160:   ISLocalToGlobalMapping ltog_f,ltog_c;
    1161:   PetscInt               m_ghost,n_ghost,m_ghost_c,n_ghost_c;
    1162:   PetscInt               row,i_start_ghost,j_start_ghost,mx,m_c,my,nc,ratioi,ratioj;
    1163:   PetscInt               i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c;
    1164:   PetscInt               *cols;
    1165:   DMBoundaryType         bx,by;
    1166:   Vec                    vecf,vecc;
    1167:   IS                     isf;

    1169:   DMDAGetInfo(dac,NULL,&Mx,&My,NULL,NULL,NULL,NULL,NULL,NULL,&bx,&by,NULL,NULL);
    1170:   DMDAGetInfo(daf,NULL,&mx,&my,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
    1171:   if (bx == DM_BOUNDARY_PERIODIC) {
    1172:     ratioi = mx/Mx;
    1174:   } else {
    1175:     ratioi = (mx-1)/(Mx-1);
    1177:   }
    1178:   if (by == DM_BOUNDARY_PERIODIC) {
    1179:     ratioj = my/My;
    1181:   } else {
    1182:     ratioj = (my-1)/(My-1);
    1184:   }

    1186:   DMDAGetCorners(daf,&i_start,&j_start,NULL,&m_f,&n_f,NULL);
    1187:   DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,NULL,&m_ghost,&n_ghost,NULL);
    1188:   DMGetLocalToGlobalMapping(daf,&ltog_f);
    1189:   ISLocalToGlobalMappingGetBlockIndices(ltog_f,&idx_f);

    1191:   DMDAGetCorners(dac,&i_start_c,&j_start_c,NULL,&m_c,&n_c,NULL);
    1192:   DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,NULL,&m_ghost_c,&n_ghost_c,NULL);
    1193:   DMGetLocalToGlobalMapping(dac,&ltog_c);
    1194:   ISLocalToGlobalMappingGetBlockIndices(ltog_c,&idx_c);

    1196:   /* loop over local fine grid nodes setting interpolation for those*/
    1197:   nc   = 0;
    1198:   PetscMalloc1(n_f*m_f,&cols);
    1199:   for (j=j_start_c; j<j_start_c+n_c; j++) {
    1200:     for (i=i_start_c; i<i_start_c+m_c; i++) {
    1201:       PetscInt i_f = i*ratioi,j_f = j*ratioj;
    1203:     j_c %D j_f %D fine ghost range [%D,%D]",j,j_f,j_start_ghost,j_start_ghost+n_ghost);
    1205:     i_c %D i_f %D fine ghost range [%D,%D]",i,i_f,i_start_ghost,i_start_ghost+m_ghost);
    1206:       row        = idx_f[(m_ghost*(j_f-j_start_ghost) + (i_f-i_start_ghost))];
    1207:       cols[nc++] = row;
    1208:     }
    1209:   }
    1210:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_f,&idx_f);
    1211:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_c,&idx_c);

    1213:   ISCreateBlock(PetscObjectComm((PetscObject)daf),dof,nc,cols,PETSC_OWN_POINTER,&isf);
    1214:   DMGetGlobalVector(dac,&vecc);
    1215:   DMGetGlobalVector(daf,&vecf);
    1216:   VecScatterCreate(vecf,isf,vecc,NULL,inject);
    1217:   DMRestoreGlobalVector(dac,&vecc);
    1218:   DMRestoreGlobalVector(daf,&vecf);
    1219:   ISDestroy(&isf);
    1220:   return 0;
    1221: }

    1223: PetscErrorCode DMCreateInjection_DA_3D(DM dac,DM daf,VecScatter *inject)
    1224: {
    1225:   PetscInt               i,j,k,i_start,j_start,k_start,m_f,n_f,p_f,Mx,My,Mz;
    1226:   PetscInt               m_ghost,n_ghost,p_ghost,m_ghost_c,n_ghost_c,p_ghost_c;
    1227:   PetscInt               i_start_ghost,j_start_ghost,k_start_ghost;
    1228:   PetscInt               mx,my,mz,ratioi,ratioj,ratiok;
    1229:   PetscInt               i_start_c,j_start_c,k_start_c;
    1230:   PetscInt               m_c,n_c,p_c;
    1231:   PetscInt               i_start_ghost_c,j_start_ghost_c,k_start_ghost_c;
    1232:   PetscInt               row,nc,dof;
    1233:   const PetscInt         *idx_c,*idx_f;
    1234:   ISLocalToGlobalMapping ltog_f,ltog_c;
    1235:   PetscInt               *cols;
    1236:   DMBoundaryType         bx,by,bz;
    1237:   Vec                    vecf,vecc;
    1238:   IS                     isf;

    1240:   DMDAGetInfo(dac,NULL,&Mx,&My,&Mz,NULL,NULL,NULL,NULL,NULL,&bx,&by,&bz,NULL);
    1241:   DMDAGetInfo(daf,NULL,&mx,&my,&mz,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);

    1243:   if (bx == DM_BOUNDARY_PERIODIC) {
    1244:     ratioi = mx/Mx;
    1246:   } else {
    1247:     ratioi = (mx-1)/(Mx-1);
    1249:   }
    1250:   if (by == DM_BOUNDARY_PERIODIC) {
    1251:     ratioj = my/My;
    1253:   } else {
    1254:     ratioj = (my-1)/(My-1);
    1256:   }
    1257:   if (bz == DM_BOUNDARY_PERIODIC) {
    1258:     ratiok = mz/Mz;
    1260:   } else {
    1261:     ratiok = (mz-1)/(Mz-1);
    1263:   }

    1265:   DMDAGetCorners(daf,&i_start,&j_start,&k_start,&m_f,&n_f,&p_f);
    1266:   DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&k_start_ghost,&m_ghost,&n_ghost,&p_ghost);
    1267:   DMGetLocalToGlobalMapping(daf,&ltog_f);
    1268:   ISLocalToGlobalMappingGetBlockIndices(ltog_f,&idx_f);

    1270:   DMDAGetCorners(dac,&i_start_c,&j_start_c,&k_start_c,&m_c,&n_c,&p_c);
    1271:   DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,&k_start_ghost_c,&m_ghost_c,&n_ghost_c,&p_ghost_c);
    1272:   DMGetLocalToGlobalMapping(dac,&ltog_c);
    1273:   ISLocalToGlobalMappingGetBlockIndices(ltog_c,&idx_c);

    1275:   /* loop over local fine grid nodes setting interpolation for those*/
    1276:   nc   = 0;
    1277:   PetscMalloc1(n_f*m_f*p_f,&cols);
    1278:   for (k=k_start_c; k<k_start_c+p_c; k++) {
    1279:     for (j=j_start_c; j<j_start_c+n_c; j++) {
    1280:       for (i=i_start_c; i<i_start_c+m_c; i++) {
    1281:         PetscInt i_f = i*ratioi,j_f = j*ratioj,k_f = k*ratiok;
    1283:                                                                           "k_c %D k_f %D fine ghost range [%D,%D]",k,k_f,k_start_ghost,k_start_ghost+p_ghost);
    1285:                                                                           "j_c %D j_f %D fine ghost range [%D,%D]",j,j_f,j_start_ghost,j_start_ghost+n_ghost);
    1287:                                                                           "i_c %D i_f %D fine ghost range [%D,%D]",i,i_f,i_start_ghost,i_start_ghost+m_ghost);
    1288:         row        = idx_f[(m_ghost*n_ghost*(k_f-k_start_ghost) + m_ghost*(j_f-j_start_ghost) + (i_f-i_start_ghost))];
    1289:         cols[nc++] = row;
    1290:       }
    1291:     }
    1292:   }
    1293:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_f,&idx_f);
    1294:   ISLocalToGlobalMappingRestoreBlockIndices(ltog_c,&idx_c);

    1296:   ISCreateBlock(PetscObjectComm((PetscObject)daf),dof,nc,cols,PETSC_OWN_POINTER,&isf);
    1297:   DMGetGlobalVector(dac,&vecc);
    1298:   DMGetGlobalVector(daf,&vecf);
    1299:   VecScatterCreate(vecf,isf,vecc,NULL,inject);
    1300:   DMRestoreGlobalVector(dac,&vecc);
    1301:   DMRestoreGlobalVector(daf,&vecf);
    1302:   ISDestroy(&isf);
    1303:   return 0;
    1304: }

    1306: PetscErrorCode  DMCreateInjection_DA(DM dac,DM daf,Mat *mat)
    1307: {
    1308:   PetscInt        dimc,Mc,Nc,Pc,mc,nc,pc,dofc,sc,dimf,Mf,Nf,Pf,mf,nf,pf,doff,sf;
    1309:   DMBoundaryType  bxc,byc,bzc,bxf,byf,bzf;
    1310:   DMDAStencilType stc,stf;
    1311:   VecScatter      inject = NULL;

    1317:   DMDAGetInfo(dac,&dimc,&Mc,&Nc,&Pc,&mc,&nc,&pc,&dofc,&sc,&bxc,&byc,&bzc,&stc);
    1318:   DMDAGetInfo(daf,&dimf,&Mf,&Nf,&Pf,&mf,&nf,&pf,&doff,&sf,&bxf,&byf,&bzf,&stf);

    1328:   if (dimc == 1) {
    1329:     DMCreateInjection_DA_1D(dac,daf,&inject);
    1330:   } else if (dimc == 2) {
    1331:     DMCreateInjection_DA_2D(dac,daf,&inject);
    1332:   } else if (dimc == 3) {
    1333:     DMCreateInjection_DA_3D(dac,daf,&inject);
    1334:   }
    1335:   MatCreateScatter(PetscObjectComm((PetscObject)inject), inject, mat);
    1336:   VecScatterDestroy(&inject);
    1337:   return 0;
    1338: }

    1340: /*@
    1341:    DMCreateAggregates - Deprecated, see DMDACreateAggregates.

    1343:    Level: intermediate
    1344: @*/
    1345: PetscErrorCode DMCreateAggregates(DM dac,DM daf,Mat *mat)
    1346: {
    1347:   return DMDACreateAggregates(dac,daf,mat);
    1348: }

    1350: /*@
    1351:    DMDACreateAggregates - Gets the aggregates that map between
    1352:    grids associated with two DMDAs.

    1354:    Collective on dmc

    1356:    Input Parameters:
    1357: +  dmc - the coarse grid DMDA
    1358: -  dmf - the fine grid DMDA

    1360:    Output Parameters:
    1361: .  rest - the restriction matrix (transpose of the projection matrix)

    1363:    Level: intermediate

    1365:    Note: This routine is not used by PETSc.
    1366:    It is not clear what its use case is and it may be removed in a future release.
    1367:    Users should contact petsc-maint@mcs.anl.gov if they plan to use it.

    1369: .seealso: DMRefine(), DMCreateInjection(), DMCreateInterpolation()
    1370: @*/
    1371: PetscErrorCode DMDACreateAggregates(DM dac,DM daf,Mat *rest)
    1372: {
    1373:   PetscErrorCode         ierr;
    1374:   PetscInt               dimc,Mc,Nc,Pc,mc,nc,pc,dofc,sc;
    1375:   PetscInt               dimf,Mf,Nf,Pf,mf,nf,pf,doff,sf;
    1376:   DMBoundaryType         bxc,byc,bzc,bxf,byf,bzf;
    1377:   DMDAStencilType        stc,stf;
    1378:   PetscInt               i,j,l;
    1379:   PetscInt               i_start,j_start,l_start, m_f,n_f,p_f;
    1380:   PetscInt               i_start_ghost,j_start_ghost,l_start_ghost,m_ghost,n_ghost,p_ghost;
    1381:   const PetscInt         *idx_f;
    1382:   PetscInt               i_c,j_c,l_c;
    1383:   PetscInt               i_start_c,j_start_c,l_start_c, m_c,n_c,p_c;
    1384:   PetscInt               i_start_ghost_c,j_start_ghost_c,l_start_ghost_c,m_ghost_c,n_ghost_c,p_ghost_c;
    1385:   const PetscInt         *idx_c;
    1386:   PetscInt               d;
    1387:   PetscInt               a;
    1388:   PetscInt               max_agg_size;
    1389:   PetscInt               *fine_nodes;
    1390:   PetscScalar            *one_vec;
    1391:   PetscInt               fn_idx;
    1392:   ISLocalToGlobalMapping ltogmf,ltogmc;

    1398:   DMDAGetInfo(dac,&dimc,&Mc,&Nc,&Pc,&mc,&nc,&pc,&dofc,&sc,&bxc,&byc,&bzc,&stc);
    1399:   DMDAGetInfo(daf,&dimf,&Mf,&Nf,&Pf,&mf,&nf,&pf,&doff,&sf,&bxf,&byf,&bzf,&stf);

    1410:   if (Pc < 0) Pc = 1;
    1411:   if (Pf < 0) Pf = 1;
    1412:   if (Nc < 0) Nc = 1;
    1413:   if (Nf < 0) Nf = 1;

    1415:   DMDAGetCorners(daf,&i_start,&j_start,&l_start,&m_f,&n_f,&p_f);
    1416:   DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&l_start_ghost,&m_ghost,&n_ghost,&p_ghost);

    1418:   DMGetLocalToGlobalMapping(daf,&ltogmf);
    1419:   ISLocalToGlobalMappingGetIndices(ltogmf,&idx_f);

    1421:   DMDAGetCorners(dac,&i_start_c,&j_start_c,&l_start_c,&m_c,&n_c,&p_c);
    1422:   DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,&l_start_ghost_c,&m_ghost_c,&n_ghost_c,&p_ghost_c);

    1424:   DMGetLocalToGlobalMapping(dac,&ltogmc);
    1425:   ISLocalToGlobalMappingGetIndices(ltogmc,&idx_c);

    1427:   /*
    1428:      Basic idea is as follows. Here's a 2D example, suppose r_x, r_y are the ratios
    1429:      for dimension 1 and 2 respectively.
    1430:      Let (i,j) be a coarse grid node. All the fine grid nodes between r_x*i and r_x*(i+1)
    1431:      and r_y*j and r_y*(j+1) will be grouped into the same coarse grid agregate.
    1432:      Each specific dof on the fine grid is mapped to one dof on the coarse grid.
    1433:   */

    1435:   max_agg_size = (Mf/Mc+1)*(Nf/Nc+1)*(Pf/Pc+1);

    1437:   /* create the matrix that will contain the restriction operator */
    1438:   MatCreateAIJ(PetscObjectComm((PetscObject)daf), m_c*n_c*p_c*dofc, m_f*n_f*p_f*doff, Mc*Nc*Pc*dofc, Mf*Nf*Pf*doff,
    1439:                       max_agg_size, NULL, max_agg_size, NULL, rest);

    1441:   /* store nodes in the fine grid here */
    1442:   PetscMalloc2(max_agg_size, &one_vec,max_agg_size, &fine_nodes);
    1443:   for (i=0; i<max_agg_size; i++) one_vec[i] = 1.0;

    1445:   /* loop over all coarse nodes */
    1446:   for (l_c=l_start_c; l_c<l_start_c+p_c; l_c++) {
    1447:     for (j_c=j_start_c; j_c<j_start_c+n_c; j_c++) {
    1448:       for (i_c=i_start_c; i_c<i_start_c+m_c; i_c++) {
    1449:         for (d=0; d<dofc; d++) {
    1450:           /* convert to local "natural" numbering and then to PETSc global numbering */
    1451:           a = idx_c[dofc*(m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c))] + d;

    1453:           fn_idx = 0;
    1454:           /* Corresponding fine points are all points (i_f, j_f, l_f) such that
    1455:              i_c*Mf/Mc <= i_f < (i_c+1)*Mf/Mc
    1456:              (same for other dimensions)
    1457:           */
    1458:           for (l=l_c*Pf/Pc; l<PetscMin((l_c+1)*Pf/Pc,Pf); l++) {
    1459:             for (j=j_c*Nf/Nc; j<PetscMin((j_c+1)*Nf/Nc,Nf); j++) {
    1460:               for (i=i_c*Mf/Mc; i<PetscMin((i_c+1)*Mf/Mc,Mf); i++) {
    1461:                 fine_nodes[fn_idx] = idx_f[doff*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))] + d;
    1462:                 fn_idx++;
    1463:               }
    1464:             }
    1465:           }
    1466:           /* add all these points to one aggregate */
    1467:           MatSetValues(*rest, 1, &a, fn_idx, fine_nodes, one_vec, INSERT_VALUES);
    1468:         }
    1469:       }
    1470:     }
    1471:   }
    1472:   ISLocalToGlobalMappingRestoreIndices(ltogmf,&idx_f);
    1473:   ISLocalToGlobalMappingRestoreIndices(ltogmc,&idx_c);
    1474:   PetscFree2(one_vec,fine_nodes);
    1475:   MatAssemblyBegin(*rest, MAT_FINAL_ASSEMBLY);
    1476:   MatAssemblyEnd(*rest, MAT_FINAL_ASSEMBLY);
    1477:   return 0;
    1478: }