Date: 2013-07-02T14:49:43+00:00

Actual source code: ex8.c
petsc-3.4.2 2013-07-02

      1: #include <petscsnes.h>
      2: #include <petscdmda.h>

      4: static char help[] = "Parallel version of the minimum surface area problem using DMs.\n\
      5: See ex10.c for the serial version. It solves a system of nonlinear equations in mixed\n\
      6: complementarity form using semismooth newton algorithm.This example is based on a\n\
      7: problem from the MINPACK-2 test suite.  Given a rectangular 2-D domain and\n\
      8: boundary values along the edges of the domain, the objective is to find the\n\
      9: surface with the minimal area that satisfies the boundary conditions.\n\
     10: This application solves this problem using complimentarity -- We are actually\n\
     11: solving the system  (grad f)_i >= 0, if x_i == l_i \n\
     12:                     (grad f)_i = 0, if l_i < x_i < u_i \n\
     13:                     (grad f)_i <= 0, if x_i == u_i  \n\
     14: where f is the function to be minimized. \n\
     15: \n\
     16: The command line options are:\n\
     17:   -da_grid_x <nx>, where <nx> = number of grid points in the 1st coordinate direction\n\
     18:   -da_grid_y <ny>, where <ny> = number of grid points in the 2nd coordinate direction\n\
     19:   -start <st>, where <st> =0 for zero vector, and an average of the boundary conditions otherwise\n\
     20:   -lb <value>, lower bound on the variables\n\
     21:   -ub <value>, upper bound on the variables\n\n";

     23: /*
     24:    User-defined application context - contains data needed by the
     25:    application-provided call-back routines, FormJacobian() and
     26:    FormFunction().
     27: */

     29: typedef struct {
     30:   DM          da;
     31:   PetscScalar *bottom, *top, *left, *right;
     32:   PetscInt    mx,my;
     33: } AppCtx;

     36: /* -------- User-defined Routines --------- */

     38: extern PetscErrorCode MSA_BoundaryConditions(AppCtx*);
     39: extern PetscErrorCode MSA_InitialPoint(AppCtx*, Vec);
     40: extern PetscErrorCode FormGradient(SNES, Vec, Vec, void*);
     41: extern PetscErrorCode FormJacobian(SNES, Vec, Mat*, Mat*, MatStructure*,void*);

     45: int main(int argc, char **argv)
     46: {
     47:   PetscErrorCode info;              /* used to check for functions returning nonzeros */
     48:   Vec            x,r;               /* solution and residual vectors */
     49:   Vec            xl,xu;             /* Bounds on the variables */
     50:   PetscBool      flg_l,flg_u;       /* flags to check if the bounds are set */
     51:   SNES           snes;              /* nonlinear solver context */
     52:   Mat            J;                 /* Jacobian matrix */
     53:   PetscInt       N;                 /* Number of elements in vector */
     54:   PetscScalar    lb = .05;
     55:   PetscScalar    ub = SNES_VI_INF;
     56:   AppCtx         user;              /* user-defined work context */
     57:   PetscBool      flg;

     59:   /* Initialize PETSc */
     60:   PetscInitialize(&argc, &argv, (char*)0, help);

     62: #if defined(PETSC_USE_COMPLEX)
     63:   SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This example does not work for scalar type complex\n");
     64: #endif

     66:   /* Check if lower and upper bounds are set */
     67:   info = PetscOptionsGetScalar(NULL, "-lb", &lb, &flg_l);CHKERRQ(info);
     68:   info = PetscOptionsGetScalar(NULL, "-ub", &ub, &flg_u);CHKERRQ(info);

     70:   /* Create distributed array to manage the 2d grid */
     71:   info = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX,-4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&user.da);CHKERRQ(info);
     72:   info = DMDAGetInfo(user.da,PETSC_IGNORE,&user.mx,&user.my,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(info);
     73:   /* Extract global vectors from DMDA; */
     74:   info = DMCreateGlobalVector(user.da,&x);CHKERRQ(info);
     75:   info = VecDuplicate(x, &r);CHKERRQ(info);

     77:   N    = user.mx*user.my;
     78:   info = DMCreateMatrix(user.da,MATAIJ,&J);CHKERRQ(info);

     80:   /* Create nonlinear solver context */
     81:   info = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(info);

     83:   /*  Set function evaluation and Jacobian evaluation  routines */
     84:   info = SNESSetFunction(snes,r,FormGradient,&user);CHKERRQ(info);
     85:   info = SNESSetJacobian(snes,J,J,FormJacobian,&user);CHKERRQ(info);

     87:   /* Set the boundary conditions */
     88:   info = MSA_BoundaryConditions(&user);CHKERRQ(info);

     90:   /* Set initial solution guess */
     91:   info = MSA_InitialPoint(&user, x);CHKERRQ(info);

     94:   /* Set Bounds on variables */
     95:   info = VecDuplicate(x, &xl);CHKERRQ(info);
     96:   info = VecDuplicate(x, &xu);CHKERRQ(info);
     97:   info = VecSet(xl, lb);CHKERRQ(info);
     98:   info = VecSet(xu, ub);CHKERRQ(info);

    100:   info = SNESVISetVariableBounds(snes,xl,xu);CHKERRQ(info);

    102:   info = SNESSetFromOptions(snes);CHKERRQ(info);

    104:   /* Solve the application */
    105:   info = SNESSolve(snes,NULL,x);CHKERRQ(info);

    107:   info = PetscOptionsHasName(NULL,"-view_sol",&flg);CHKERRQ(info);
    108:   if (flg) { info = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(info); }

    110:   /* Free memory */
    111:   info = VecDestroy(&x);CHKERRQ(info);
    112:   info = VecDestroy(&xl);CHKERRQ(info);
    113:   info = VecDestroy(&xu);CHKERRQ(info);
    114:   info = VecDestroy(&r);CHKERRQ(info);
    115:   info = MatDestroy(&J);CHKERRQ(info);
    116:   info = SNESDestroy(&snes);CHKERRQ(info);

    118:   /* Free user-created data structures */
    119:   info = DMDestroy(&user.da);CHKERRQ(info);
    120:   info = PetscFree(user.bottom);CHKERRQ(info);
    121:   info = PetscFree(user.top);CHKERRQ(info);
    122:   info = PetscFree(user.left);CHKERRQ(info);
    123:   info = PetscFree(user.right);CHKERRQ(info);

    125:   info = PetscFinalize();

    127:   return 0;
    128: }

    130: /* -------------------------------------------------------------------- */

    134: /*  FormGradient - Evaluates gradient of f.

    136:     Input Parameters:
    137: .   snes  - the SNES context
    138: .   X     - input vector
    139: .   ptr   - optional user-defined context, as set by SNESSetFunction()

    141:     Output Parameters:
    142: .   G - vector containing the newly evaluated gradient
    143: */
    144: PetscErrorCode FormGradient(SNES snes, Vec X, Vec G, void *ptr)
    145: {
    146:   AppCtx      *user = (AppCtx*) ptr;
    147:   int         info;
    148:   PetscInt    i,j;
    149:   PetscInt    mx=user->mx, my=user->my;
    150:   PetscScalar hx=1.0/(mx+1),hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
    151:   PetscScalar f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
    152:   PetscScalar df1dxc,df2dxc,df3dxc,df4dxc,df5dxc,df6dxc;
    153:   PetscScalar **g, **x;
    154:   PetscInt    xs,xm,ys,ym;
    155:   Vec         localX;

    158:   /* Initialize vector to zero */
    159:   info = VecSet(G,0.0);CHKERRQ(info);

    161:   /* Get local vector */
    162:   info = DMGetLocalVector(user->da,&localX);CHKERRQ(info);
    163:   /* Get ghost points */
    164:   info = DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);CHKERRQ(info);
    165:   info = DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);CHKERRQ(info);
    166:   /* Get pointer to local vector data */
    167:   info = DMDAVecGetArray(user->da,localX, &x);CHKERRQ(info);
    168:   info = DMDAVecGetArray(user->da,G, &g);CHKERRQ(info);

    170:   info = DMDAGetCorners(user->da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(info);
    171:   /* Compute function over the locally owned part of the mesh */
    172:   for (j=ys; j < ys+ym; j++) {
    173:     for (i=xs; i< xs+xm; i++) {

    175:       xc = x[j][i];
    176:       xlt=xrb=xl=xr=xb=xt=xc;

    178:       if (i==0) { /* left side */
    179:         xl  = user->left[j+1];
    180:         xlt = user->left[j+2];
    181:       } else xl = x[j][i-1];

    183:       if (j==0) { /* bottom side */
    184:         xb  = user->bottom[i+1];
    185:         xrb = user->bottom[i+2];
    186:       } else xb = x[j-1][i];

    188:       if (i+1 == mx) { /* right side */
    189:         xr  = user->right[j+1];
    190:         xrb = user->right[j];
    191:       } else xr = x[j][i+1];

    193:       if (j+1==0+my) { /* top side */
    194:         xt  = user->top[i+1];
    195:         xlt = user->top[i];
    196:       } else xt = x[j+1][i];

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

    201:       d1 = (xc-xl);
    202:       d2 = (xc-xr);
    203:       d3 = (xc-xt);
    204:       d4 = (xc-xb);
    205:       d5 = (xr-xrb);
    206:       d6 = (xrb-xb);
    207:       d7 = (xlt-xl);
    208:       d8 = (xt-xlt);

    210:       df1dxc = d1*hydhx;
    211:       df2dxc = (d1*hydhx + d4*hxdhy);
    212:       df3dxc = d3*hxdhy;
    213:       df4dxc = (d2*hydhx + d3*hxdhy);
    214:       df5dxc = d2*hydhx;
    215:       df6dxc = d4*hxdhy;

    217:       d1 /= hx;
    218:       d2 /= hx;
    219:       d3 /= hy;
    220:       d4 /= hy;
    221:       d5 /= hy;
    222:       d6 /= hx;
    223:       d7 /= hy;
    224:       d8 /= hx;

    226:       f1 = PetscSqrtReal(1.0 + d1*d1 + d7*d7);
    227:       f2 = PetscSqrtReal(1.0 + d1*d1 + d4*d4);
    228:       f3 = PetscSqrtReal(1.0 + d3*d3 + d8*d8);
    229:       f4 = PetscSqrtReal(1.0 + d3*d3 + d2*d2);
    230:       f5 = PetscSqrtReal(1.0 + d2*d2 + d5*d5);
    231:       f6 = PetscSqrtReal(1.0 + d4*d4 + d6*d6);

    233:       df1dxc /= f1;
    234:       df2dxc /= f2;
    235:       df3dxc /= f3;
    236:       df4dxc /= f4;
    237:       df5dxc /= f5;
    238:       df6dxc /= f6;

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

    242:     }
    243:   }

    245:   /* Restore vectors */
    246:   info = DMDAVecRestoreArray(user->da,localX, &x);CHKERRQ(info);
    247:   info = DMDAVecRestoreArray(user->da,G, &g);CHKERRQ(info);
    248:   info = DMRestoreLocalVector(user->da,&localX);CHKERRQ(info);
    249:   info = PetscLogFlops(67*mx*my);CHKERRQ(info);
    250:   return(0);
    251: }

    253: /* ------------------------------------------------------------------- */
    256: /*
    257:    FormJacobian - Evaluates Jacobian matrix.

    259:    Input Parameters:
    260: .  snes - SNES context
    261: .  X    - input vector
    262: .  ptr  - optional user-defined context, as set by SNESSetJacobian()

    264:    Output Parameters:
    265: .  tH    - Jacobian matrix

    267: */
    268: PetscErrorCode FormJacobian(SNES snes, Vec X, Mat *tH, Mat *tHPre, MatStructure *flag, void *ptr)
    269: {
    270:   AppCtx         *user = (AppCtx*) ptr;
    271:   Mat            H     = *tH;
    272:   PetscErrorCode info;
    273:   PetscInt       i,j,k;
    274:   PetscInt       mx=user->mx, my=user->my;
    275:   MatStencil     row,col[7];
    276:   PetscScalar    hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
    277:   PetscScalar    f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
    278:   PetscScalar    hl,hr,ht,hb,hc,htl,hbr;
    279:   PetscScalar    **x, v[7];
    280:   PetscBool      assembled;
    281:   PetscInt       xs,xm,ys,ym;
    282:   Vec            localX;

    285:   /* Set various matrix options */
    286:   info = MatAssembled(H,&assembled);CHKERRQ(info);
    287:   if (assembled) {info = MatZeroEntries(H);CHKERRQ(info);}
    288:   *flag=SAME_NONZERO_PATTERN;

    290:   /* Get local vector */
    291:   info = DMGetLocalVector(user->da,&localX);CHKERRQ(info);
    292:   /* Get ghost points */
    293:   info = DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);CHKERRQ(info);
    294:   info = DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);CHKERRQ(info);

    296:   /* Get pointers to vector data */
    297:   info = DMDAVecGetArray(user->da,localX, &x);CHKERRQ(info);

    299:   info = DMDAGetCorners(user->da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(info);
    300:   /* Compute Jacobian over the locally owned part of the mesh */
    301:   for (j=ys; j< ys+ym; j++) {
    302:     for (i=xs; i< xs+xm; i++) {
    303:       xc = x[j][i];
    304:       xlt=xrb=xl=xr=xb=xt=xc;

    306:       /* Left */
    307:       if (i==0) {
    308:         xl  = user->left[j+1];
    309:         xlt = user->left[j+2];
    310:       } else xl = x[j][i-1];

    312:       /* Bottom */
    313:       if (j==0) {
    314:         xb  = user->bottom[i+1];
    315:         xrb = user->bottom[i+2];
    316:       } else xb = x[j-1][i];

    318:       /* Right */
    319:       if (i+1 == mx) {
    320:         xr  = user->right[j+1];
    321:         xrb = user->right[j];
    322:       } else xr = x[j][i+1];

    324:       /* Top */
    325:       if (j+1==my) {
    326:         xt  = user->top[i+1];
    327:         xlt = user->top[i];
    328:       } else xt = x[j+1][i];

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

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

    336:       d1 = (xc-xl)/hx;
    337:       d2 = (xc-xr)/hx;
    338:       d3 = (xc-xt)/hy;
    339:       d4 = (xc-xb)/hy;
    340:       d5 = (xrb-xr)/hy;
    341:       d6 = (xrb-xb)/hx;
    342:       d7 = (xlt-xl)/hy;
    343:       d8 = (xlt-xt)/hx;

    345:       f1 = PetscSqrtReal(1.0 + d1*d1 + d7*d7);
    346:       f2 = PetscSqrtReal(1.0 + d1*d1 + d4*d4);
    347:       f3 = PetscSqrtReal(1.0 + d3*d3 + d8*d8);
    348:       f4 = PetscSqrtReal(1.0 + d3*d3 + d2*d2);
    349:       f5 = PetscSqrtReal(1.0 + d2*d2 + d5*d5);
    350:       f6 = PetscSqrtReal(1.0 + d4*d4 + d6*d6);

    353:       hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
    354:            (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
    355:       hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
    356:            (-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
    357:       ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
    358:            (-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
    359:       hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
    360:            (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);

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

    365:       hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
    366:            hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
    367:            (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) +
    368:            (hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4);

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

    372:       k     =0;
    373:       row.i = i;row.j= j;
    374:       /* Bottom */
    375:       if (j>0) {
    376:         v[k]     =hb;
    377:         col[k].i = i; col[k].j=j-1; k++;
    378:       }

    380:       /* Bottom right */
    381:       if (j>0 && i < mx -1) {
    382:         v[k]     =hbr;
    383:         col[k].i = i+1; col[k].j = j-1; k++;
    384:       }

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

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

    395:       /* Right */
    396:       if (i < mx-1) {
    397:         v[k]    = hr;
    398:         col[k].i= i+1; col[k].j = j;k++;
    399:       }

    401:       /* Top left */
    402:       if (i>0 && j < my-1) {
    403:         v[k]     = htl;
    404:         col[k].i = i-1;col[k].j = j+1; k++;
    405:       }

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

    413:       info = MatSetValuesStencil(H,1,&row,k,col,v,INSERT_VALUES);CHKERRQ(info);
    414:     }
    415:   }

    417:   /* Assemble the matrix */
    418:   info = MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);CHKERRQ(info);
    419:   info = DMDAVecRestoreArray(user->da,localX,&x);CHKERRQ(info);
    420:   info = MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);CHKERRQ(info);
    421:   info = DMRestoreLocalVector(user->da,&localX);CHKERRQ(info);

    423:   info = PetscLogFlops(199*mx*my);CHKERRQ(info);
    424:   return(0);
    425: }

    427: /* ------------------------------------------------------------------- */
    430: /*
    431:    MSA_BoundaryConditions -  Calculates the boundary conditions for
    432:    the region.

    434:    Input Parameter:
    435: .  user - user-defined application context

    437:    Output Parameter:
    438: .  user - user-defined application context
    439: */
    440: PetscErrorCode MSA_BoundaryConditions(AppCtx * user)
    441: {
    442:   PetscErrorCode info;
    443:   PetscInt       i,j,k,limit=0,maxits=5;
    444:   PetscInt       mx   =user->mx,my=user->my;
    445:   PetscInt       bsize=0, lsize=0, tsize=0, rsize=0;
    446:   PetscScalar    one  =1.0, two=2.0, three=3.0, tol=1e-10;
    447:   PetscScalar    fnorm,det,hx,hy,xt=0,yt=0;
    448:   PetscScalar    u1,u2,nf1,nf2,njac11,njac12,njac21,njac22;
    449:   PetscScalar    b=-0.5, t=0.5, l=-0.5, r=0.5;
    450:   PetscScalar    *boundary;

    453:   bsize=mx+2; lsize=my+2; rsize=my+2; tsize=mx+2;

    455:   info = PetscMalloc(bsize*sizeof(PetscScalar), &user->bottom);CHKERRQ(info);
    456:   info = PetscMalloc(tsize*sizeof(PetscScalar), &user->top);CHKERRQ(info);
    457:   info = PetscMalloc(lsize*sizeof(PetscScalar), &user->left);CHKERRQ(info);
    458:   info = PetscMalloc(rsize*sizeof(PetscScalar), &user->right);CHKERRQ(info);

    460:   hx= (r-l)/(mx+1); hy=(t-b)/(my+1);

    462:   for (j=0; j<4; j++) {
    463:     if (j==0) {
    464:       yt       = b;
    465:       xt       = l;
    466:       limit    = bsize;
    467:       boundary = user->bottom;
    468:     } else if (j==1) {
    469:       yt       = t;
    470:       xt       = l;
    471:       limit    = tsize;
    472:       boundary = user->top;
    473:     } else if (j==2) {
    474:       yt       = b;
    475:       xt       = l;
    476:       limit    = lsize;
    477:       boundary = user->left;
    478:     } else { /* if  (j==3) */
    479:       yt       = b;
    480:       xt       = r;
    481:       limit    = rsize;
    482:       boundary = user->right;
    483:     }

    485:     for (i=0; i<limit; i++) {
    486:       u1=xt;
    487:       u2=-yt;
    488:       for (k=0; k<maxits; k++) {
    489:         nf1   = u1 + u1*u2*u2 - u1*u1*u1/three-xt;
    490:         nf2   = -u2 - u1*u1*u2 + u2*u2*u2/three-yt;
    491:         fnorm = PetscSqrtReal(nf1*nf1+nf2*nf2);
    492:         if (fnorm <= tol) break;
    493:         njac11 = one+u2*u2-u1*u1;
    494:         njac12 = two*u1*u2;
    495:         njac21 = -two*u1*u2;
    496:         njac22 = -one - u1*u1 + u2*u2;
    497:         det    = njac11*njac22-njac21*njac12;
    498:         u1     = u1-(njac22*nf1-njac12*nf2)/det;
    499:         u2     = u2-(njac11*nf2-njac21*nf1)/det;
    500:       }

    502:       boundary[i]=u1*u1-u2*u2;
    503:       if (j==0 || j==1) xt=xt+hx;
    504:       else yt=yt+hy; /* if (j==2 || j==3) */
    505:     }
    506:   }
    507:   return(0);
    508: }

    510: /* ------------------------------------------------------------------- */
    513: /*
    514:    MSA_InitialPoint - Calculates the initial guess in one of three ways.

    516:    Input Parameters:
    517: .  user - user-defined application context
    518: .  X - vector for initial guess

    520:    Output Parameters:
    521: .  X - newly computed initial guess
    522: */
    523: PetscErrorCode MSA_InitialPoint(AppCtx * user, Vec X)
    524: {
    525:   PetscErrorCode info;
    526:   PetscInt       start=-1,i,j;
    527:   PetscScalar    zero =0.0;
    528:   PetscBool      flg;

    531:   info = PetscOptionsGetInt(NULL,"-start",&start,&flg);CHKERRQ(info);

    533:   if (flg && start==0) { /* The zero vector is reasonable */

    535:     info = VecSet(X, zero);CHKERRQ(info);
    536:     /* PLogInfo(user,"Min. Surface Area Problem: Start with 0 vector \n"); */

    539:   } else { /* Take an average of the boundary conditions */
    540:     PetscInt    mx=user->mx,my=user->my;
    541:     PetscScalar **x;
    542:     PetscInt    xs,xm,ys,ym;

    544:     /* Get pointers to vector data */
    545:     info = DMDAVecGetArray(user->da,X,&x);CHKERRQ(info);
    546:     info = DMDAGetCorners(user->da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(info);

    548:     /* Perform local computations */
    549:     for (j=ys; j<ys+ym; j++) {
    550:       for (i=xs; i< xs+xm; i++) {
    551:         x[j][i] = (((j+1)*user->bottom[i+1]+(my-j+1)*user->top[i+1])/(my+2)+
    552:                    ((i+1)*user->left[j+1]+(mx-i+1)*user->right[j+1])/(mx+2))/2.0;
    553:       }
    554:     }

    556:     /* Restore vectors */
    557:     info = DMDAVecRestoreArray(user->da,X,&x);CHKERRQ(info);

    559:   }
    560:   return(0);
    561: }