Actual source code: ex58.c

petsc-master 2018-02-22
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  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*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*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*/