Actual source code: ex58.c

petsc-master 2017-09-23
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  1:  #include <petscsnes.h>
  2:  #include <petscdm.h>
  3:  #include <petscdmda.h>

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

 24: /*
 25:    User-defined application context - contains data needed by the
 26:    application-provided call-back routines, FormJacobian() and
 27:    FormFunction().
 28: */

 30: /*
 31:      This is a new version of the ../tests/ex8.c code

 33:      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

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

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


 42: */

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


 50: /* -------- User-defined Routines --------- */

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

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

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

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

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

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

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

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

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

 91:   SNESSetComputeInitialGuess(snes,ComputeInitialGuess,NULL);

 93:   SNESVISetComputeVariableBounds(snes,FormBounds);

 95:   SNESSetFromOptions(snes);

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

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

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

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

113: /* -------------------------------------------------------------------- */

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

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

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

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

136: /* -------------------------------------------------------------------- */

138: /*  FormGradient - Evaluates gradient of f.

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

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

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

168:   VecSet(G,0.0);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

251:     }
252:   }

254:   /* Restore vectors */
255:   DMDAVecRestoreArray(da,localX, &x);
256:   DMDAVecRestoreArray(da,G, &g);
257:   DMRestoreLocalVector(da,&localX);
258:   PetscLogFlops(67*mx*my);
259:   return(0);
260: }

262: /* ------------------------------------------------------------------- */
263: /*
264:    FormJacobian - Evaluates Jacobian matrix.

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

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

274: */
275: PetscErrorCode FormJacobian(SNES snes, Vec X, Mat H, Mat tHPre, void *ptr)
276: {
277:   AppCtx         *user;
279:   PetscInt       i,j,k;
280:   PetscInt       mx, my;
281:   MatStencil     row,col[7];
282:   PetscScalar    hx, hy, hydhx, hxdhy;
283:   PetscScalar    f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
284:   PetscScalar    hl,hr,ht,hb,hc,htl,hbr;
285:   PetscScalar    **x, v[7];
286:   PetscBool      assembled;
287:   PetscInt       xs,xm,ys,ym;
288:   Vec            localX;
289:   DM             da;

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

434:   PetscLogFlops(199*mx*my);
435:   return(0);
436: }

438: /* ------------------------------------------------------------------- */
439: /*
440:    FormBoundaryConditions -  Calculates the boundary conditions for
441:    the region.

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

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

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

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

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

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

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

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

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

532: PetscErrorCode DestroyBoundaryConditions(AppCtx **ouser)
533: {
535:   AppCtx         *user = *ouser;

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


547: /* ------------------------------------------------------------------- */
548: /*
549:    ComputeInitialGuess - Calculates the initial guess

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

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

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

571:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
572:   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);

574:   /* Get pointers to vector data */
575:   DMDAVecGetArray(da,X,&x);
576:   /* Perform local computations */
577:   for (j=ys; j<ys+ym; j++) {
578:     for (i=xs; i< xs+xm; i++) {
579:       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;
580:     }
581:   }
582:   /* Restore vectors */
583:   DMDAVecRestoreArray(da,X,&x);
584:   return(0);
585: }