Actual source code: ex58.c

      2: #include <petscsnes.h>
      3: #include <petscdm.h>
      4: #include <petscdmda.h>

      6: static const char help[] = "Parallel version of the minimum surface area problem in 2D using DMDA.\n\
      7:  It solves a system of nonlinear equations in mixed\n\
      8: complementarity form.This example is based on a\n\
      9: problem from the MINPACK-2 test suite.  Given a rectangular 2-D domain and\n\
     10: boundary values along the edges of the domain, the objective is to find the\n\
     11: surface with the minimal area that satisfies the boundary conditions.\n\
     12: This application solves this problem using complimentarity -- We are actually\n\
     13: solving the system  (grad f)_i >= 0, if x_i == l_i \n\
     14:                     (grad f)_i = 0, if l_i < x_i < u_i \n\
     15:                     (grad f)_i <= 0, if x_i == u_i  \n\
     16: where f is the function to be minimized. \n\
     17: \n\
     18: The command line options are:\n\
     19:   -da_grid_x <nx>, where <nx> = number of grid points in the 1st coordinate direction\n\
     20:   -da_grid_y <ny>, where <ny> = number of grid points in the 2nd coordinate direction\n\
     21:   -start <st>, where <st> =0 for zero vector, and an average of the boundary conditions otherwise\n\
     22:   -lb <value>, lower bound on the variables\n\
     23:   -ub <value>, upper bound on the variables\n\n";

     25: /*
     26:    User-defined application context - contains data needed by the
     27:    application-provided call-back routines, FormJacobian() and
     28:    FormFunction().
     29: */

     31: /*
     32:      This is a new version of the ../tests/ex8.c code

     34:      Run, for example, with the options ./ex58 -snes_vi_monitor -ksp_monitor -mg_levels_ksp_monitor -pc_type mg -pc_mg_levels 2 -pc_mg_galerkin pmat -ksp_type fgmres

     36:      Or to run with grid sequencing on the nonlinear problem (note that you do not need to provide the number of
     37:          multigrid levels, it will be determined automatically based on the number of refinements done)

     39:       ./ex58 -pc_type mg -ksp_monitor  -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3
     40:              -mg_levels_ksp_monitor -snes_vi_monitor -mg_levels_pc_type sor -pc_mg_type full

     43: */

     45: typedef struct {
     46:   PetscScalar *bottom, *top, *left, *right;
     47:   PetscScalar lb,ub;
     48: } AppCtx;

     51: /* -------- User-defined Routines --------- */

     53: extern PetscErrorCode FormBoundaryConditions(SNES,AppCtx**);
     54: extern PetscErrorCode DestroyBoundaryConditions(AppCtx**);
     55: extern PetscErrorCode ComputeInitialGuess(SNES, Vec,void*);
     56: extern PetscErrorCode FormGradient(SNES, Vec, Vec, void*);
     57: extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void*);
     58: extern PetscErrorCode FormBounds(SNES,Vec,Vec);

     60: int main(int argc, char **argv)
     61: {
     63:   Vec            x,r;               /* solution and residual vectors */
     64:   SNES           snes;              /* nonlinear solver context */
     65:   Mat            J;                 /* Jacobian matrix */
     66:   DM             da;

     68:   PetscInitialize(&argc, &argv, (char*)0, help);if (ierr) return ierr;

     70:   /* Create distributed array to manage the 2d grid */
     71:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
     72:   DMSetFromOptions(da);
     73:   DMSetUp(da);

     75:   /* Extract global vectors from DMDA; */
     76:   DMCreateGlobalVector(da,&x);
     77:   VecDuplicate(x, &r);

     79:   DMSetMatType(da,MATAIJ);
     80:   DMCreateMatrix(da,&J);

     82:   /* Create nonlinear solver context */
     83:   SNESCreate(PETSC_COMM_WORLD,&snes);
     84:   SNESSetDM(snes,da);

     86:   /*  Set function evaluation and Jacobian evaluation  routines */
     87:   SNESSetFunction(snes,r,FormGradient,NULL);
     88:   SNESSetJacobian(snes,J,J,FormJacobian,NULL);

     90:   SNESSetComputeApplicationContext(snes,(PetscErrorCode (*)(SNES,void**))FormBoundaryConditions,(PetscErrorCode (*)(void**))DestroyBoundaryConditions);

     92:   SNESSetComputeInitialGuess(snes,ComputeInitialGuess,NULL);

     94:   SNESVISetComputeVariableBounds(snes,FormBounds);

     96:   SNESSetFromOptions(snes);

     98:   /* Solve the application */
     99:   SNESSolve(snes,NULL,x);

    101:   /* Free memory */
    102:   VecDestroy(&x);
    103:   VecDestroy(&r);
    104:   MatDestroy(&J);
    105:   SNESDestroy(&snes);

    107:   /* Free user-created data structures */
    108:   DMDestroy(&da);

    110:   PetscFinalize();
    111:   return ierr;
    112: }

    114: /* -------------------------------------------------------------------- */

    116: /*  FormBounds - sets the upper and lower bounds

    118:     Input Parameters:
    119: .   snes  - the SNES context

    121:     Output Parameters:
    122: .   xl - lower bounds
    123: .   xu - upper bounds
    124: */
    125: PetscErrorCode FormBounds(SNES snes, Vec xl, Vec xu)
    126: {
    128:   AppCtx         *ctx;

    131:   SNESGetApplicationContext(snes,&ctx);
    132:   VecSet(xl,ctx->lb);
    133:   VecSet(xu,ctx->ub);
    134:   return(0);
    135: }

    137: /* -------------------------------------------------------------------- */

    139: /*  FormGradient - Evaluates gradient of f.

    141:     Input Parameters:
    142: .   snes  - the SNES context
    143: .   X     - input vector
    144: .   ptr   - optional user-defined context, as set by SNESSetFunction()

    146:     Output Parameters:
    147: .   G - vector containing the newly evaluated gradient
    148: */
    149: PetscErrorCode FormGradient(SNES snes, Vec X, Vec G, void *ptr)
    150: {
    151:   AppCtx      *user;
    152:   int         ierr;
    153:   PetscInt    i,j;
    154:   PetscInt    mx, my;
    155:   PetscScalar hx,hy, hydhx, hxdhy;
    156:   PetscScalar f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
    157:   PetscScalar df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc;
    158:   PetscScalar **g, **x;
    159:   PetscInt    xs,xm,ys,ym;
    160:   Vec         localX;
    161:   DM          da;

    164:   SNESGetDM(snes,&da);
    165:   SNESGetApplicationContext(snes,(void**)&user);
    166:   DMDAGetInfo(da,PETSC_IGNORE,&mx,&my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
    167:   hx   = 1.0/(mx+1);hy=1.0/(my+1); hydhx=hy/hx; hxdhy=hx/hy;

    169:   VecSet(G,0.0);

    171:   /* Get local vector */
    172:   DMGetLocalVector(da,&localX);
    173:   /* Get ghost points */
    174:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    175:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);
    176:   /* Get pointer to local vector data */
    177:   DMDAVecGetArray(da,localX, &x);
    178:   DMDAVecGetArray(da,G, &g);

    180:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
    181:   /* Compute function over the locally owned part of the mesh */
    182:   for (j=ys; j < ys+ym; j++) {
    183:     for (i=xs; i< xs+xm; i++) {

    185:       xc = x[j][i];
    186:       xlt=xrb=xl=xr=xb=xt=xc;

    188:       if (i==0) { /* left side */
    189:         xl  = user->left[j+1];
    190:         xlt = user->left[j+2];
    191:       } else xl = x[j][i-1];

    193:       if (j==0) { /* bottom side */
    194:         xb  = user->bottom[i+1];
    195:         xrb = user->bottom[i+2];
    196:       } else xb = x[j-1][i];

    198:       if (i+1 == mx) { /* right side */
    199:         xr  = user->right[j+1];
    200:         xrb = user->right[j];
    201:       } else xr = x[j][i+1];

    203:       if (j+1==0+my) { /* top side */
    204:         xt  = user->top[i+1];
    205:         xlt = user->top[i];
    206:       } else xt = x[j+1][i];

    208:       if (i>0 && j+1<my) xlt = x[j+1][i-1]; /* left top side */
    209:       if (j>0 && i+1<mx) xrb = x[j-1][i+1]; /* right bottom */

    211:       d1 = (xc-xl);
    212:       d2 = (xc-xr);
    213:       d3 = (xc-xt);
    214:       d4 = (xc-xb);
    215:       d5 = (xr-xrb);
    216:       d6 = (xrb-xb);
    217:       d7 = (xlt-xl);
    218:       d8 = (xt-xlt);

    220:       df1dxc = d1*hydhx;
    221:       df2dxc = (d1*hydhx + d4*hxdhy);
    222:       df3dxc = d3*hxdhy;
    223:       df4dxc = (d2*hydhx + d3*hxdhy);
    224:       df5dxc = d2*hydhx;
    225:       df6dxc = d4*hxdhy;

    227:       d1 /= hx;
    228:       d2 /= hx;
    229:       d3 /= hy;
    230:       d4 /= hy;
    231:       d5 /= hy;
    232:       d6 /= hx;
    233:       d7 /= hy;
    234:       d8 /= hx;

    236:       f1 = PetscSqrtScalar(1.0 + d1*d1 + d7*d7);
    237:       f2 = PetscSqrtScalar(1.0 + d1*d1 + d4*d4);
    238:       f3 = PetscSqrtScalar(1.0 + d3*d3 + d8*d8);
    239:       f4 = PetscSqrtScalar(1.0 + d3*d3 + d2*d2);
    240:       f5 = PetscSqrtScalar(1.0 + d2*d2 + d5*d5);
    241:       f6 = PetscSqrtScalar(1.0 + d4*d4 + d6*d6);

    243:       df1dxc /= f1;
    244:       df2dxc /= f2;
    245:       df3dxc /= f3;
    246:       df4dxc /= f4;
    247:       df5dxc /= f5;
    248:       df6dxc /= f6;

    250:       g[j][i] = (df1dxc+df2dxc+df3dxc+df4dxc+df5dxc+df6dxc)/2.0;

    252:     }
    253:   }

    255:   /* Restore vectors */
    256:   DMDAVecRestoreArray(da,localX, &x);
    257:   DMDAVecRestoreArray(da,G, &g);
    258:   DMRestoreLocalVector(da,&localX);
    259:   PetscLogFlops(67.0*mx*my);
    260:   return(0);
    261: }

    263: /* ------------------------------------------------------------------- */
    264: /*
    265:    FormJacobian - Evaluates Jacobian matrix.

    267:    Input Parameters:
    268: .  snes - SNES context
    269: .  X    - input vector
    270: .  ptr  - optional user-defined context, as set by SNESSetJacobian()

    272:    Output Parameters:
    273: .  tH    - Jacobian matrix

    275: */
    276: PetscErrorCode FormJacobian(SNES snes, Vec X, Mat H, Mat tHPre, void *ptr)
    277: {
    278:   AppCtx         *user;
    280:   PetscInt       i,j,k;
    281:   PetscInt       mx, my;
    282:   MatStencil     row,col[7];
    283:   PetscScalar    hx, hy, hydhx, hxdhy;
    284:   PetscScalar    f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
    285:   PetscScalar    hl,hr,ht,hb,hc,htl,hbr;
    286:   PetscScalar    **x, v[7];
    287:   PetscBool      assembled;
    288:   PetscInt       xs,xm,ys,ym;
    289:   Vec            localX;
    290:   DM             da;

    293:   SNESGetDM(snes,&da);
    294:   SNESGetApplicationContext(snes,(void**)&user);
    295:   DMDAGetInfo(da,PETSC_IGNORE,&mx,&my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
    296:   hx   = 1.0/(mx+1); hy=1.0/(my+1); hydhx=hy/hx; hxdhy=hx/hy;

    298: /* Set various matrix options */
    299:   MatAssembled(H,&assembled);
    300:   if (assembled) {MatZeroEntries(H);}

    302:   /* Get local vector */
    303:   DMGetLocalVector(da,&localX);
    304:   /* Get ghost points */
    305:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
    306:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

    308:   /* Get pointers to vector data */
    309:   DMDAVecGetArray(da,localX, &x);

    311:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
    312:   /* Compute Jacobian over the locally owned part of the mesh */
    313:   for (j=ys; j< ys+ym; j++) {
    314:     for (i=xs; i< xs+xm; i++) {
    315:       xc = x[j][i];
    316:       xlt=xrb=xl=xr=xb=xt=xc;

    318:       /* Left */
    319:       if (i==0) {
    320:         xl  = user->left[j+1];
    321:         xlt = user->left[j+2];
    322:       } else xl = x[j][i-1];

    324:       /* Bottom */
    325:       if (j==0) {
    326:         xb  =user->bottom[i+1];
    327:         xrb = user->bottom[i+2];
    328:       } else xb = x[j-1][i];

    330:       /* Right */
    331:       if (i+1 == mx) {
    332:         xr  =user->right[j+1];
    333:         xrb = user->right[j];
    334:       } else xr = x[j][i+1];

    336:       /* Top */
    337:       if (j+1==my) {
    338:         xt  =user->top[i+1];
    339:         xlt = user->top[i];
    340:       } else xt = x[j+1][i];

    342:       /* Top left */
    343:       if (i>0 && j+1<my) xlt = x[j+1][i-1];

    345:       /* Bottom right */
    346:       if (j>0 && i+1<mx) xrb = x[j-1][i+1];

    348:       d1 = (xc-xl)/hx;
    349:       d2 = (xc-xr)/hx;
    350:       d3 = (xc-xt)/hy;
    351:       d4 = (xc-xb)/hy;
    352:       d5 = (xrb-xr)/hy;
    353:       d6 = (xrb-xb)/hx;
    354:       d7 = (xlt-xl)/hy;
    355:       d8 = (xlt-xt)/hx;

    357:       f1 = PetscSqrtScalar(1.0 + d1*d1 + d7*d7);
    358:       f2 = PetscSqrtScalar(1.0 + d1*d1 + d4*d4);
    359:       f3 = PetscSqrtScalar(1.0 + d3*d3 + d8*d8);
    360:       f4 = PetscSqrtScalar(1.0 + d3*d3 + d2*d2);
    361:       f5 = PetscSqrtScalar(1.0 + d2*d2 + d5*d5);
    362:       f6 = PetscSqrtScalar(1.0 + d4*d4 + d6*d6);

    365:       hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
    366:            (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
    367:       hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
    368:            (-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
    369:       ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
    370:            (-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
    371:       hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
    372:            (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);

    374:       hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
    375:       htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);

    377:       hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
    378:            hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
    379:            (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2.0*d1*d4)/(f2*f2*f2) +
    380:            (hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2.0*d2*d3)/(f4*f4*f4);

    382:       hl/=2.0; hr/=2.0; ht/=2.0; hb/=2.0; hbr/=2.0; htl/=2.0;  hc/=2.0;

    384:       k     =0;
    385:       row.i = i;row.j= j;
    386:       /* Bottom */
    387:       if (j>0) {
    388:         v[k]     =hb;
    389:         col[k].i = i; col[k].j=j-1; k++;
    390:       }

    392:       /* Bottom right */
    393:       if (j>0 && i < mx -1) {
    394:         v[k]     =hbr;
    395:         col[k].i = i+1; col[k].j = j-1; k++;
    396:       }

    398:       /* left */
    399:       if (i>0) {
    400:         v[k]     = hl;
    401:         col[k].i = i-1; col[k].j = j; k++;
    402:       }

    404:       /* Centre */
    405:       v[k]= hc; col[k].i= row.i; col[k].j = row.j; k++;

    407:       /* Right */
    408:       if (i < mx-1) {
    409:         v[k]    = hr;
    410:         col[k].i= i+1; col[k].j = j;k++;
    411:       }

    413:       /* Top left */
    414:       if (i>0 && j < my-1) {
    415:         v[k]     = htl;
    416:         col[k].i = i-1;col[k].j = j+1; k++;
    417:       }

    419:       /* Top */
    420:       if (j < my-1) {
    421:         v[k]     = ht;
    422:         col[k].i = i; col[k].j = j+1; k++;
    423:       }

    425:       MatSetValuesStencil(H,1,&row,k,col,v,INSERT_VALUES);
    426:     }
    427:   }

    429:   /* Assemble the matrix */
    430:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
    431:   DMDAVecRestoreArray(da,localX,&x);
    432:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
    433:   DMRestoreLocalVector(da,&localX);

    435:   PetscLogFlops(199.0*mx*my);
    436:   return(0);
    437: }

    439: /* ------------------------------------------------------------------- */
    440: /*
    441:    FormBoundaryConditions -  Calculates the boundary conditions for
    442:    the region.

    444:    Input Parameter:
    445: .  user - user-defined application context

    447:    Output Parameter:
    448: .  user - user-defined application context
    449: */
    450: PetscErrorCode FormBoundaryConditions(SNES snes,AppCtx **ouser)
    451: {
    453:   PetscInt       i,j,k,limit=0,maxits=5;
    454:   PetscInt       mx,my;
    455:   PetscInt       bsize=0, lsize=0, tsize=0, rsize=0;
    456:   PetscScalar    one  =1.0, two=2.0, three=3.0;
    457:   PetscScalar    det,hx,hy,xt=0,yt=0;
    458:   PetscReal      fnorm, tol=1e-10;
    459:   PetscScalar    u1,u2,nf1,nf2,njac11,njac12,njac21,njac22;
    460:   PetscScalar    b=-0.5, t=0.5, l=-0.5, r=0.5;
    461:   PetscScalar    *boundary;
    462:   AppCtx         *user;
    463:   DM             da;

    466:   SNESGetDM(snes,&da);
    467:   PetscNew(&user);
    468:   *ouser   = user;
    469:   user->lb = .05;
    470:   user->ub = PETSC_INFINITY;
    471:   DMDAGetInfo(da,PETSC_IGNORE,&mx,&my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    473:   /* Check if lower and upper bounds are set */
    474:   PetscOptionsGetScalar(NULL,NULL, "-lb", &user->lb, 0);
    475:   PetscOptionsGetScalar(NULL,NULL, "-ub", &user->ub, 0);
    476:   bsize=mx+2; lsize=my+2; rsize=my+2; tsize=mx+2;

    478:   PetscMalloc1(bsize, &user->bottom);
    479:   PetscMalloc1(tsize, &user->top);
    480:   PetscMalloc1(lsize, &user->left);
    481:   PetscMalloc1(rsize, &user->right);

    483:   hx= (r-l)/(mx+1.0); hy=(t-b)/(my+1.0);

    485:   for (j=0; j<4; j++) {
    486:     if (j==0) {
    487:       yt       = b;
    488:       xt       = l;
    489:       limit    = bsize;
    490:       boundary = user->bottom;
    491:     } else if (j==1) {
    492:       yt       = t;
    493:       xt       = l;
    494:       limit    = tsize;
    495:       boundary = user->top;
    496:     } else if (j==2) {
    497:       yt       = b;
    498:       xt       = l;
    499:       limit    = lsize;
    500:       boundary = user->left;
    501:     } else { /* if  (j==3) */
    502:       yt       = b;
    503:       xt       = r;
    504:       limit    = rsize;
    505:       boundary = user->right;
    506:     }

    508:     for (i=0; i<limit; i++) {
    509:       u1=xt;
    510:       u2=-yt;
    511:       for (k=0; k<maxits; k++) {
    512:         nf1   = u1 + u1*u2*u2 - u1*u1*u1/three-xt;
    513:         nf2   = -u2 - u1*u1*u2 + u2*u2*u2/three-yt;
    514:         fnorm = PetscRealPart(PetscSqrtScalar(nf1*nf1+nf2*nf2));
    515:         if (fnorm <= tol) break;
    516:         njac11=one+u2*u2-u1*u1;
    517:         njac12=two*u1*u2;
    518:         njac21=-two*u1*u2;
    519:         njac22=-one - u1*u1 + u2*u2;
    520:         det   = njac11*njac22-njac21*njac12;
    521:         u1    = u1-(njac22*nf1-njac12*nf2)/det;
    522:         u2    = u2-(njac11*nf2-njac21*nf1)/det;
    523:       }

    525:       boundary[i]=u1*u1-u2*u2;
    526:       if (j==0 || j==1) xt=xt+hx;
    527:       else yt=yt+hy; /* if (j==2 || j==3) */
    528:     }
    529:   }
    530:   return(0);
    531: }

    533: PetscErrorCode DestroyBoundaryConditions(AppCtx **ouser)
    534: {
    536:   AppCtx         *user = *ouser;

    539:   PetscFree(user->bottom);
    540:   PetscFree(user->top);
    541:   PetscFree(user->left);
    542:   PetscFree(user->right);
    543:   PetscFree(*ouser);
    544:   return(0);
    545: }

    548: /* ------------------------------------------------------------------- */
    549: /*
    550:    ComputeInitialGuess - Calculates the initial guess

    552:    Input Parameters:
    553: .  user - user-defined application context
    554: .  X - vector for initial guess

    556:    Output Parameters:
    557: .  X - newly computed initial guess
    558: */
    559: PetscErrorCode ComputeInitialGuess(SNES snes, Vec X,void *dummy)
    560: {
    562:   PetscInt       i,j,mx,my;
    563:   DM             da;
    564:   AppCtx         *user;
    565:   PetscScalar    **x;
    566:   PetscInt       xs,xm,ys,ym;

    569:   SNESGetDM(snes,&da);
    570:   SNESGetApplicationContext(snes,(void**)&user);

    572:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
    573:   DMDAGetInfo(da,PETSC_IGNORE,&mx,&my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

    575:   /* Get pointers to vector data */
    576:   DMDAVecGetArray(da,X,&x);
    577:   /* Perform local computations */
    578:   for (j=ys; j<ys+ym; j++) {
    579:     for (i=xs; i< xs+xm; i++) {
    580:       x[j][i] = (((j+1.0)*user->bottom[i+1]+(my-j+1.0)*user->top[i+1])/(my+2.0)+((i+1.0)*user->left[j+1]+(mx-i+1.0)*user->right[j+1])/(mx+2.0))/2.0;
    581:     }
    582:   }
    583:   /* Restore vectors */
    584:   DMDAVecRestoreArray(da,X,&x);
    585:   return(0);
    586: }

    589: /*TEST

    591:    test:
    592:       args: -snes_type vinewtonrsls -pc_type mg -ksp_monitor_short -pc_mg_galerkin pmat -da_refine 5 -snes_vi_monitor -pc_mg_type full -snes_max_it 100 -snes_converged_reason
    593:       requires: !single

    595:    test:
    596:       suffix: 2
    597:       args: -snes_type vinewtonssls -pc_type mg -ksp_monitor_short -pc_mg_galerkin pmat -da_refine 5 -snes_vi_monitor -pc_mg_type full -snes_max_it 100 -snes_converged_reason
    598:       requires: !single

    600: TEST*/