Actual source code: ex58.c

petsc-dev 2014-02-02
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  1: #include <petscsnes.h>
  2: #include <petscdmda.h>

  4: static const char help[] = "Parallel version of the minimum surface area problem in 2D using DMDA.\n\
  5:  It solves a system of nonlinear equations in mixed\n\
  6: complementarity form.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: /*
 30:      This is a new version of the ../tests/ex8.c code

 32:      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 -ksp_type fgmres

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

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


 41: */

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


 49: /* -------- User-defined Routines --------- */

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

 70:   /* Create distributed array to manage the 2d grid */
 71:   DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX,-4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);

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

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

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

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

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

 90:   SNESSetComputeInitialGuess(snes,ComputeInitialGuess,NULL);

 92:   SNESVISetComputeVariableBounds(snes,FormBounds);

 94:   SNESSetFromOptions(snes);

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

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

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

108:   PetscFinalize();
109:   return 0;
110: }

112: /* -------------------------------------------------------------------- */

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

141: /*  FormGradient - Evaluates gradient of f.

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

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

166:   SNESGetDM(snes,&da);
167:   SNESGetApplicationContext(snes,(void**)&user);
168:   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);
169:   hx   = 1.0/(mx+1);hy=1.0/(my+1); hydhx=hy/hx; hxdhy=hx/hy;

171:   VecSet(G,0.0);

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

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

187:       xc = x[j][i];
188:       xlt=xrb=xl=xr=xb=xt=xc;

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

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

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

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

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

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

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

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

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

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

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

254:     }
255:   }

257:   /* Restore vectors */
258:   DMDAVecRestoreArray(da,localX, &x);
259:   DMDAVecRestoreArray(da,G, &g);
260:   DMRestoreLocalVector(da,&localX);
261:   PetscLogFlops(67*mx*my);
262:   return(0);
263: }

265: /* ------------------------------------------------------------------- */
268: /*
269:    FormJacobian - Evaluates Jacobian matrix.

271:    Input Parameters:
272: .  snes - SNES context
273: .  X    - input vector
274: .  ptr  - optional user-defined context, as set by SNESSetJacobian()

276:    Output Parameters:
277: .  tH    - Jacobian matrix

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

298:   SNESGetDM(snes,&da);
299:   SNESGetApplicationContext(snes,(void**)&user);
300:   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);
301:   hx   = 1.0/(mx+1); hy=1.0/(my+1); hydhx=hy/hx; hxdhy=hx/hy;

303: /* Set various matrix options */
304:   MatAssembled(H,&assembled);
305:   if (assembled) {MatZeroEntries(H);}
306:   *flag=SAME_NONZERO_PATTERN;

308:   /* Get local vector */
309:   DMGetLocalVector(da,&localX);
310:   /* Get ghost points */
311:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
312:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

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

317:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
318:   /* Compute Jacobian over the locally owned part of the mesh */
319:   for (j=ys; j< ys+ym; j++) {
320:     for (i=xs; i< xs+xm; i++) {
321:       xc = x[j][i];
322:       xlt=xrb=xl=xr=xb=xt=xc;

324:       /* Left */
325:       if (i==0) {
326:         xl  = user->left[j+1];
327:         xlt = user->left[j+2];
328:       } else xl = x[j][i-1];

330:       /* Bottom */
331:       if (j==0) {
332:         xb  =user->bottom[i+1];
333:         xrb = user->bottom[i+2];
334:       } else xb = x[j-1][i];

336:       /* Right */
337:       if (i+1 == mx) {
338:         xr  =user->right[j+1];
339:         xrb = user->right[j];
340:       } else xr = x[j][i+1];

342:       /* Top */
343:       if (j+1==my) {
344:         xt  =user->top[i+1];
345:         xlt = user->top[i];
346:       } else xt = x[j+1][i];

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

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

354:       d1 = (xc-xl)/hx;
355:       d2 = (xc-xr)/hx;
356:       d3 = (xc-xt)/hy;
357:       d4 = (xc-xb)/hy;
358:       d5 = (xrb-xr)/hy;
359:       d6 = (xrb-xb)/hx;
360:       d7 = (xlt-xl)/hy;
361:       d8 = (xlt-xt)/hx;

363:       f1 = PetscSqrtScalar(1.0 + d1*d1 + d7*d7);
364:       f2 = PetscSqrtScalar(1.0 + d1*d1 + d4*d4);
365:       f3 = PetscSqrtScalar(1.0 + d3*d3 + d8*d8);
366:       f4 = PetscSqrtScalar(1.0 + d3*d3 + d2*d2);
367:       f5 = PetscSqrtScalar(1.0 + d2*d2 + d5*d5);
368:       f6 = PetscSqrtScalar(1.0 + d4*d4 + d6*d6);


371:       hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
372:            (-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
373:       hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
374:            (-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
375:       ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
376:            (-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
377:       hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
378:            (-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);

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

383:       hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
384:            hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
385:            (hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2.0*d1*d4)/(f2*f2*f2) +
386:            (hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2.0*d2*d3)/(f4*f4*f4);

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

390:       k     =0;
391:       row.i = i;row.j= j;
392:       /* Bottom */
393:       if (j>0) {
394:         v[k]     =hb;
395:         col[k].i = i; col[k].j=j-1; k++;
396:       }

398:       /* Bottom right */
399:       if (j>0 && i < mx -1) {
400:         v[k]     =hbr;
401:         col[k].i = i+1; col[k].j = j-1; k++;
402:       }

404:       /* left */
405:       if (i>0) {
406:         v[k]     = hl;
407:         col[k].i = i-1; col[k].j = j; k++;
408:       }

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

413:       /* Right */
414:       if (i < mx-1) {
415:         v[k]    = hr;
416:         col[k].i= i+1; col[k].j = j;k++;
417:       }

419:       /* Top left */
420:       if (i>0 && j < my-1) {
421:         v[k]     = htl;
422:         col[k].i = i-1;col[k].j = j+1; k++;
423:       }

425:       /* Top */
426:       if (j < my-1) {
427:         v[k]     = ht;
428:         col[k].i = i; col[k].j = j+1; k++;
429:       }

431:       MatSetValuesStencil(H,1,&row,k,col,v,INSERT_VALUES);
432:     }
433:   }

435:   /* Assemble the matrix */
436:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
437:   DMDAVecRestoreArray(da,localX,&x);
438:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
439:   DMRestoreLocalVector(da,&localX);

441:   PetscLogFlops(199*mx*my);
442:   return(0);
443: }

445: /* ------------------------------------------------------------------- */
448: /*
449:    FormBoundaryConditions -  Calculates the boundary conditions for
450:    the region.

452:    Input Parameter:
453: .  user - user-defined application context

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

474:   SNESGetDM(snes,&da);
475:   PetscNew(&user);
476:   *ouser   = user;
477:   user->lb = .05;
478:   user->ub = PETSC_INFINITY;
479:   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);

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

486:   PetscMalloc1(bsize, &user->bottom);
487:   PetscMalloc1(tsize, &user->top);
488:   PetscMalloc1(lsize, &user->left);
489:   PetscMalloc1(rsize, &user->right);

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

493:   for (j=0; j<4; j++) {
494:     if (j==0) {
495:       yt       = b;
496:       xt       = l;
497:       limit    = bsize;
498:       boundary = user->bottom;
499:     } else if (j==1) {
500:       yt       = t;
501:       xt       = l;
502:       limit    = tsize;
503:       boundary = user->top;
504:     } else if (j==2) {
505:       yt       = b;
506:       xt       = l;
507:       limit    = lsize;
508:       boundary = user->left;
509:     } else { /* if  (j==3) */
510:       yt       = b;
511:       xt       = r;
512:       limit    = rsize;
513:       boundary = user->right;
514:     }

516:     for (i=0; i<limit; i++) {
517:       u1=xt;
518:       u2=-yt;
519:       for (k=0; k<maxits; k++) {
520:         nf1   = u1 + u1*u2*u2 - u1*u1*u1/three-xt;
521:         nf2   = -u2 - u1*u1*u2 + u2*u2*u2/three-yt;
522:         fnorm = PetscRealPart(PetscSqrtScalar(nf1*nf1+nf2*nf2));
523:         if (fnorm <= tol) break;
524:         njac11=one+u2*u2-u1*u1;
525:         njac12=two*u1*u2;
526:         njac21=-two*u1*u2;
527:         njac22=-one - u1*u1 + u2*u2;
528:         det   = njac11*njac22-njac21*njac12;
529:         u1    = u1-(njac22*nf1-njac12*nf2)/det;
530:         u2    = u2-(njac11*nf2-njac21*nf1)/det;
531:       }

533:       boundary[i]=u1*u1-u2*u2;
534:       if (j==0 || j==1) xt=xt+hx;
535:       else yt=yt+hy; /* if (j==2 || j==3) */
536:     }
537:   }
538:   return(0);
539: }

543: PetscErrorCode DestroyBoundaryConditions(AppCtx **ouser)
544: {
546:   AppCtx         *user = *ouser;

549:   PetscFree(user->bottom);
550:   PetscFree(user->top);
551:   PetscFree(user->left);
552:   PetscFree(user->right);
553:   PetscFree(*ouser);
554:   return(0);
555: }


558: /* ------------------------------------------------------------------- */
561: /*
562:    ComputeInitialGuess - Calculates the initial guess

564:    Input Parameters:
565: .  user - user-defined application context
566: .  X - vector for initial guess

568:    Output Parameters:
569: .  X - newly computed initial guess
570: */
571: PetscErrorCode ComputeInitialGuess(SNES snes, Vec X,void *dummy)
572: {
574:   PetscInt       i,j,mx,my;
575:   DM             da;
576:   AppCtx         *user;
577:   PetscScalar    **x;
578:   PetscInt       xs,xm,ys,ym;

581:   SNESGetDM(snes,&da);
582:   SNESGetApplicationContext(snes,(void**)&user);

584:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
585:   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);

587:   /* Get pointers to vector data */
588:   DMDAVecGetArray(da,X,&x);
589:   /* Perform local computations */
590:   for (j=ys; j<ys+ym; j++) {
591:     for (i=xs; i< xs+xm; i++) {
592:       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;
593:     }
594:   }
595:   /* Restore vectors */
596:   DMDAVecRestoreArray(da,X,&x);
597:   return(0);
598: }