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: }