Actual source code: ex63.c

petsc-dev 2014-07-25
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  1: static char help[] = "1D coupled Allen-Cahn and Cahn-Hilliard equation for degenerate mobility and triangular elements.\n\
  2: Runtime options include:\n\
  3: -xmin <xmin>\n\
  4: -xmax <xmax>\n\
  5: -ymin <ymin>\n\
  6: -T <T>, where <T> is the end time for the time domain simulation\n\
  7: -dt <dt>,where <dt> is the step size for the numerical integration\n\
  8: -gamma <gamma>\n\
  9: -theta_c <theta_c>\n\n";

 11: /*
 12: ./ex63 -ksp_type fgmres -snes_vi_monitor   -snes_atol 1.e-11 -snes_converged_reason -ksp_converged_reason   -snes_linesearch_monitor -VG 10000000 -draw_fields 1,3,4  -pc_type mg -pc_mg_galerkin -log_summary -dt .000001 -mg_coarse_pc_type svd  -ksp_monitor_true_residual -ksp_rtol 1.e-9 -snes_linesearch basic -T .0020 -P_casc .0005 -snes_monitor_solution -da_refine 10
 13:  */

 15: #include <petscsnes.h>
 16: #include <petscdmda.h>

 18: typedef struct {
 19:   PetscReal   dt,T; /* Time step and end time */
 20:   DM          da1,da1_clone,da2;
 21:   Mat         M;    /* Jacobian matrix */
 22:   Mat         M_0;
 23:   Vec         q,wv,cv,wi,ci,eta,cvi,DPsiv,DPsii,DPsieta,Pv,Pi,Piv,logcv,logci,logcvi,Riv;
 24:   Vec         work1,work2,work3,work4;
 25:   PetscScalar Dv,Di,Evf,Eif,A,kBT,kav,kai,kaeta,Rsurf,Rbulk,L,P_casc,VG; /* physics parameters */
 26:   PetscReal   xmin,xmax,ymin,ymax;
 27:   PetscInt    nx;
 28:   PetscBool   voidgrowth;
 29:   PetscBool   degenerate;
 30:   PetscBool   graphics;
 31:   PetscReal   smallnumber;
 32:   PetscReal   initv;
 33:   PetscReal   initeta;
 34: } AppCtx;

 36: PetscErrorCode GetParams(AppCtx*);
 37: PetscErrorCode SetRandomVectors(AppCtx*);
 38: PetscErrorCode SetVariableBounds(DM,Vec,Vec);
 39: PetscErrorCode SetUpMatrices(AppCtx*);
 40: PetscErrorCode UpdateMatrices(AppCtx*);
 41: PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
 42: PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);
 43: PetscErrorCode SetInitialGuess(Vec,AppCtx*);
 44: PetscErrorCode Update_q(AppCtx*);
 45: PetscErrorCode Update_u(Vec,AppCtx*);
 46: PetscErrorCode DPsi(AppCtx*);
 47: PetscErrorCode Llog(Vec,Vec);
 48: PetscErrorCode CheckRedundancy(SNES,IS,IS*,DM);

 52: int main(int argc, char **argv)
 53: {
 55:   Vec            x,r;  /* Solution and residual vectors */
 56:   SNES           snes; /* Nonlinear solver context */
 57:   AppCtx         user; /* Application context */
 58:   Vec            xl,xu; /* Upper and lower bounds on variables */
 59:   Mat            J;
 60:   PetscScalar    t=0.0;
 61:   PetscViewer    view_out, view_p, view_q, view_psi, view_mat;
 62:   PetscReal      bounds[] = {1000.0,-1000.,0.0,1.0,1000.0,-1000.0,0.0,1.0,1000.0,-1000.0};


 65:   PetscInitialize(&argc,&argv, (char*)0, help);

 67:   /* Get physics and time parameters */
 68:   GetParams(&user);
 69:   /* Create a 1D DA with dof = 5; the whole thing */
 70:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC, -4, 5, 1,NULL,&user.da1);
 71:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC, -4, 5, 1,NULL,&user.da1_clone);
 72:   /* Create a 1D DA with dof = 1; for individual componentes */
 73:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC, -4, 1, 1,NULL,&user.da2);

 75:   /* Set Element type (triangular) */
 76:   DMDASetElementType(user.da1,DMDA_ELEMENT_P1);
 77:   DMDASetElementType(user.da2,DMDA_ELEMENT_P1);

 79:   /* Set x and y coordinates */
 80:   DMDASetUniformCoordinates(user.da1,user.xmin,user.xmax,NULL,NULL,NULL,NULL);
 81:   DMDASetUniformCoordinates(user.da2,user.xmin,user.xmax,NULL,NULL,NULL,NULL);
 82:   /* Get global vector x from DM (da1) and duplicate vectors r,xl,xu */
 83:   DMCreateGlobalVector(user.da1,&x);
 84:   VecDuplicate(x,&r);
 85:   VecDuplicate(x,&xl);
 86:   VecDuplicate(x,&xu);
 87:   VecDuplicate(x,&user.q);

 89:   /* Get global vector user->wv from da2 and duplicate other vectors */
 90:   DMCreateGlobalVector(user.da2,&user.wv);
 91:   VecDuplicate(user.wv,&user.cv);
 92:   VecDuplicate(user.wv,&user.wi);
 93:   VecDuplicate(user.wv,&user.ci);
 94:   VecDuplicate(user.wv,&user.eta);
 95:   VecDuplicate(user.wv,&user.cvi);
 96:   VecDuplicate(user.wv,&user.DPsiv);
 97:   VecDuplicate(user.wv,&user.DPsii);
 98:   VecDuplicate(user.wv,&user.DPsieta);
 99:   VecDuplicate(user.wv,&user.Pv);
100:   VecDuplicate(user.wv,&user.Pi);
101:   VecDuplicate(user.wv,&user.Piv);
102:   VecDuplicate(user.wv,&user.Riv);
103:   VecDuplicate(user.wv,&user.logcv);
104:   VecDuplicate(user.wv,&user.logci);
105:   VecDuplicate(user.wv,&user.logcvi);
106:   VecDuplicate(user.wv,&user.work1);
107:   VecDuplicate(user.wv,&user.work2);
108:   VecDuplicate(user.wv,&user.work3);
109:   VecDuplicate(user.wv,&user.work4);

111:   /* Get Jacobian matrix structure from the da for the entire thing, da1 */
112:   DMSetMatType(user.da1,MATAIJ);
113:   DMCreateMatrix(user.da1,&user.M);
114:   /* Get the (usual) mass matrix structure from da2 */
115:   DMSetMatType(user.da2,MATAIJ);
116:   DMCreateMatrix(user.da2,&user.M_0);
117:   SetInitialGuess(x,&user);
118:   /* Form the jacobian matrix and M_0 */
119:   SetUpMatrices(&user);
120:   MatDuplicate(user.M,MAT_DO_NOT_COPY_VALUES,&J);

122:   SNESCreate(PETSC_COMM_WORLD,&snes);
123:   SNESSetDM(snes,user.da1);

125:   SNESSetFunction(snes,r,FormFunction,(void*)&user);
126:   SNESSetJacobian(snes,J,J,FormJacobian,(void*)&user);

128:   SetVariableBounds(user.da1,xl,xu);
129:   SNESVISetVariableBounds(snes,xl,xu);
130:   SNESSetFromOptions(snes);
131:   /* SNESVISetRedundancyCheck(snes,(PetscErrorCode (*)(SNES,IS,IS*,void*))CheckRedundancy,user.da1_clone); */
132:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_out",FILE_MODE_WRITE,&view_out);
133:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_p",FILE_MODE_WRITE,&view_p);
134:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_q",FILE_MODE_WRITE,&view_q);
135:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_psi",FILE_MODE_WRITE,&view_psi);
136:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_mat",FILE_MODE_WRITE,&view_mat);
137:   /* PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),5,bounds); */

139:   if (user.graphics) {
140:     PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),5,bounds);

142:     VecView(x,PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD));
143:   }
144:   while (t<user.T) {
145:     char        filename[PETSC_MAX_PATH_LEN];
146:     PetscScalar a = 1.0;
147:     PetscInt    i;
148:     PetscViewer view;


151:     SNESSetFunction(snes,r,FormFunction,(void*)&user);
152:     SNESSetJacobian(snes,J,J,FormJacobian,(void*)&user);

154:     SetRandomVectors(&user);
155:     DPsi(&user);
156:     VecView(user.DPsiv,view_psi);
157:     VecView(user.DPsii,view_psi);
158:     VecView(user.DPsieta,view_psi);

160:     VecView(user.Pv,view_p);
161:     Update_q(&user);
162:     VecView(user.q,view_q);
163:     MatView(user.M,view_mat);
164:     SNESSolve(snes,NULL,x);

166:     VecView(x,view_out);
167:     if (user.graphics) {
168:       VecView(x,PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD));
169:     }

171:     PetscInt its;
172:     SNESGetIterationNumber(snes,&its);
173:     PetscPrintf(PETSC_COMM_WORLD,"SNESVI solver converged at t = %5.4g in %d iterations\n",t,its);

175:     Update_u(x,&user);
176:     for (i=0; i < (int)(user.T/a) ; i++) {
177:       if (t/a > i - user.dt/a && t/a < i + user.dt/a) {
178:         sprintf(filename,"output_%f",t);
179:         PetscViewerBinaryOpen(PETSC_COMM_WORLD,filename,FILE_MODE_WRITE,&view);
180:         VecView(user.cv,view);
181:         VecView(user.ci,view);
182:         VecView(user.eta,view);
183:         PetscViewerDestroy(&view);
184:       }
185:     }
186:     UpdateMatrices(&user);
187:     t    = t + user.dt;

189:   }


192:   PetscViewerDestroy(&view_out);
193:   PetscViewerDestroy(&view_p);
194:   PetscViewerDestroy(&view_q);
195:   PetscViewerDestroy(&view_psi);
196:   PetscViewerDestroy(&view_mat);
197:   VecDestroy(&x);
198:   VecDestroy(&r);
199:   VecDestroy(&xl);
200:   VecDestroy(&xu);
201:   VecDestroy(&user.q);
202:   VecDestroy(&user.wv);
203:   VecDestroy(&user.cv);
204:   VecDestroy(&user.wi);
205:   VecDestroy(&user.ci);
206:   VecDestroy(&user.eta);
207:   VecDestroy(&user.cvi);
208:   VecDestroy(&user.DPsiv);
209:   VecDestroy(&user.DPsii);
210:   VecDestroy(&user.DPsieta);
211:   VecDestroy(&user.Pv);
212:   VecDestroy(&user.Pi);
213:   VecDestroy(&user.Piv);
214:   VecDestroy(&user.Riv);
215:   VecDestroy(&user.logcv);
216:   VecDestroy(&user.logci);
217:   VecDestroy(&user.logcvi);
218:   VecDestroy(&user.work1);
219:   VecDestroy(&user.work2);
220:   VecDestroy(&user.work3);
221:   VecDestroy(&user.work4);
222:   MatDestroy(&user.M);
223:   MatDestroy(&user.M_0);
224:   DMDestroy(&user.da1);
225:   DMDestroy(&user.da1_clone);
226:   DMDestroy(&user.da2);
227:   SNESDestroy(&snes);
228:   PetscFinalize();
229:   return 0;
230: }

234: PetscErrorCode Update_u(Vec X,AppCtx *user)
235: {
237:   PetscInt       i,n;
238:   PetscScalar    *xx,*wv_p,*cv_p,*wi_p,*ci_p,*eta_p;
239:   PetscInt       pv1,pi1,peta1,pv2,pi2,peta2;
240:   PetscReal      maxv,maxi,maxeta,minv,mini,mineta;


244:   VecGetLocalSize(user->wv,&n);


247:   VecMax(user->cv,&pv1,&maxv);
248:   VecMax(user->ci,&pi1,&maxi);
249:   VecMax(user->eta,&peta1,&maxeta);
250:   VecMin(user->cv,&pv2,&minv);
251:   VecMin(user->ci,&pi2,&mini);
252:   VecMin(user->eta,&peta2,&mineta);


255:   VecGetArray(X,&xx);
256:   VecGetArray(user->wv,&wv_p);
257:   VecGetArray(user->cv,&cv_p);
258:   VecGetArray(user->wi,&wi_p);
259:   VecGetArray(user->ci,&ci_p);
260:   VecGetArray(user->eta,&eta_p);


263:   for (i=0; i<n; i++) {
264:     wv_p[i]  = xx[5*i];
265:     cv_p[i]  = xx[5*i+1];
266:     wi_p[i]  = xx[5*i+2];
267:     ci_p[i]  = xx[5*i+3];
268:     eta_p[i] = xx[5*i+4];
269:   }
270:   VecRestoreArray(X,&xx);
271:   VecRestoreArray(user->wv,&wv_p);
272:   VecRestoreArray(user->cv,&cv_p);
273:   VecRestoreArray(user->wi,&wi_p);
274:   VecRestoreArray(user->ci,&ci_p);
275:   VecRestoreArray(user->eta,&eta_p);
276:   return(0);
277: }

281: PetscErrorCode Update_q(AppCtx *user)
282: {
284:   PetscScalar    *q_p, *w1, *w2;
285:   PetscInt       i,n;
286:   PetscScalar    norm1;

289:   VecPointwiseMult(user->Riv,user->eta,user->eta);
290:   VecScale(user->Riv,user->Rsurf);
291:   VecShift(user->Riv,user->Rbulk);
292:   VecPointwiseMult(user->Riv,user->ci,user->Riv);
293:   VecPointwiseMult(user->Riv,user->cv,user->Riv);

295:   VecCopy(user->Riv,user->work1);
296:   VecScale(user->work1,user->dt);
297:   VecAXPY(user->work1,-1.0,user->cv);
298:   MatMult(user->M_0,user->work1,user->work2);

300:   VecGetArray(user->q,&q_p);
301:   VecGetArray(user->work1,&w1);
302:   VecGetArray(user->work2,&w2);
303:   VecGetLocalSize(user->wv,&n);
304:   for (i=0; i<n; i++) q_p[5*i]=w2[i];

306:   MatMult(user->M_0,user->DPsiv,user->work1);
307:   for (i=0; i<n; i++) q_p[5*i+1]=w1[i];

309:   VecCopy(user->Riv,user->work1);
310:   VecScale(user->work1,user->dt);
311:   VecAXPY(user->work1,-1.0,user->ci);
312:   MatMult(user->M_0,user->work1,user->work2);
313:   for (i=0; i<n; i++) q_p[5*i+2]=w2[i];

315:   MatMult(user->M_0,user->DPsii,user->work1);
316:   for (i=0; i<n; i++) q_p[5*i+3]=w1[i];

318:   VecCopy(user->DPsieta,user->work1);
319:   VecScale(user->work1,user->L);
320:   VecAXPY(user->work1,-1.0/user->dt,user->eta);
321:   MatMult(user->M_0,user->work1,user->work2);
322:   for (i=0; i<n; i++) q_p[5*i+4]=w2[i];

324:   VecRestoreArray(user->q,&q_p);
325:   VecRestoreArray(user->work1,&w1);
326:   VecRestoreArray(user->work2,&w2);
327:   return(0);
328: }

332: PetscErrorCode DPsi(AppCtx *user)
333: {
335:   PetscScalar    Evf=user->Evf,Eif=user->Eif,kBT=user->kBT,A=user->A;
336:   PetscScalar    *cv_p,*ci_p,*eta_p,*logcv_p,*logci_p,*logcvi_p,*DPsiv_p,*DPsii_p,*DPsieta_p;
337:   PetscInt       n,i;

340:   VecGetLocalSize(user->cv,&n);
341:   VecGetArray(user->cv,&cv_p);
342:   VecGetArray(user->ci,&ci_p);
343:   VecGetArray(user->eta,&eta_p);
344:   VecGetArray(user->logcv,&logcv_p);
345:   VecGetArray(user->logci,&logci_p);
346:   VecGetArray(user->logcvi,&logcvi_p);
347:   VecGetArray(user->DPsiv,&DPsiv_p);
348:   VecGetArray(user->DPsii,&DPsii_p);
349:   VecGetArray(user->DPsieta,&DPsieta_p);

351:   Llog(user->cv,user->logcv);
352:   Llog(user->ci,user->logci);

354:   VecCopy(user->cv,user->cvi);
355:   VecAXPY(user->cvi,1.0,user->ci);
356:   VecScale(user->cvi,-1.0);
357:   VecShift(user->cvi,1.0);
358:   Llog(user->cvi,user->logcvi);

360:   for (i=0; i<n; i++)
361:   {
362:     DPsiv_p[i] = (eta_p[i]-1.0)*(eta_p[i]-1.0)*(Evf + kBT*(logcv_p[i] - logcvi_p[i])) + eta_p[i]*eta_p[i]*2*A*(cv_p[i]-1);
363:     DPsii_p[i] = (eta_p[i]-1.0)*(eta_p[i]-1.0)*(Eif + kBT*(logci_p[i] - logcvi_p[i])) + eta_p[i]*eta_p[i]*2*A*ci_p[i];

365:     DPsieta_p[i] = 2.0*(eta_p[i]-1.0)*(Evf*cv_p[i] + Eif*ci_p[i] + kBT*(cv_p[i]* logcv_p[i] + ci_p[i]* logci_p[i] + (1-cv_p[i]-ci_p[i])*logcvi_p[i])) + 2.0*eta_p[i]*A*((cv_p[i]-1.0)*(cv_p[i]-1.0) + ci_p[i]*ci_p[i]);
366:   }

368:   VecRestoreArray(user->cv,&cv_p);
369:   VecRestoreArray(user->ci,&ci_p);
370:   VecRestoreArray(user->eta,&eta_p);
371:   VecGetArray(user->logcv,&logcv_p);
372:   VecGetArray(user->logci,&logci_p);
373:   VecGetArray(user->logcvi,&logcvi_p);
374:   VecRestoreArray(user->DPsiv,&DPsiv_p);
375:   VecRestoreArray(user->DPsii,&DPsii_p);
376:   VecRestoreArray(user->DPsieta,&DPsieta_p);
377:   return(0);

379: }


384: PetscErrorCode Llog(Vec X, Vec Y)
385: {
387:   PetscScalar    *x,*y;
388:   PetscInt       n,i;

391:   VecGetArray(X,&x);
392:   VecGetArray(Y,&y);
393:   VecGetLocalSize(X,&n);
394:   for (i=0; i<n; i++) {
395:     if (x[i] < 1.0e-12) y[i] = log(1.0e-12);
396:     else y[i] = log(x[i]);
397:   }
398:   return(0);
399: }

403: PetscErrorCode SetInitialGuess(Vec X,AppCtx *user)
404: {

407:   PetscInt          n,i,Mda;
408:   PetscScalar       *xx,*cv_p,*ci_p,*wv_p,*wi_p,*eta_p;
409:   PetscViewer       view_out;
410:   /* needed for the void growth case */
411:   PetscScalar       xmid,cv_v=1.0,cv_m=0.122,ci_v=0.0,ci_m=.00069,eta_v=1.0,eta_m=0.0,h,lambda;
412:   PetscInt          nele,nen,idx[2];
413:   const PetscInt    *ele;
414:   PetscScalar       x[2];
415:   Vec               coords;
416:   const PetscScalar *_coords;
417:   PetscViewer       view;
418:   PetscScalar       xwidth = user->xmax - user->xmin;

421:   VecGetLocalSize(X,&n);

423:   if (user->voidgrowth) {
424:     DMDAGetInfo(user->da2,NULL,&Mda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
425:     DMGetCoordinatesLocal(user->da2,&coords);
426:     VecGetArrayRead(coords,&_coords);

428:     h      = (user->xmax-user->xmin)/Mda;
429:     xmid   = (user->xmax + user->xmin)/2.0;
430:     lambda = 4.0*h;

432:     DMDAGetElements(user->da2,&nele,&nen,&ele);
433:     for (i=0; i < nele; i++) {
434:       idx[0] = ele[2*i]; idx[1] = ele[2*i+1];

436:       x[0] = _coords[idx[0]];
437:       x[1] = _coords[idx[1]];


440:       PetscInt    k;
441:       PetscScalar vals_cv[2],vals_ci[2],vals_eta[2],s,hhr,r;
442:       for (k=0; k < 2; k++) {
443:         s = PetscAbs(x[k] - xmid);
444:         if (s < xwidth*(5.0/64.0)) {
445:           vals_cv[k]  = cv_v;
446:           vals_ci[k]  = ci_v;
447:           vals_eta[k] = eta_v;
448:         } else if (s>= xwidth*(5.0/64.0) && s<= xwidth*(7.0/64.0)) {
449:           /* r = (s - xwidth*(6.0/64.0))/(0.5*lambda); */
450:           r           = (s - xwidth*(6.0/64.0))/(xwidth/64.0);
451:           hhr         = 0.25*(-r*r*r + 3*r + 2);
452:           vals_cv[k]  = cv_m + (1.0 - hhr)*(cv_v - cv_m);
453:           vals_ci[k]  = ci_m + (1.0 - hhr)*(ci_v - ci_m);
454:           vals_eta[k] = eta_m + (1.0 - hhr)*(eta_v - eta_m);
455:         } else {
456:           vals_cv[k]  = cv_m;
457:           vals_ci[k]  = ci_m;
458:           vals_eta[k] = eta_m;
459:         }
460:       }

462:       VecSetValuesLocal(user->cv,2,idx,vals_cv,INSERT_VALUES);
463:       VecSetValuesLocal(user->ci,2,idx,vals_ci,INSERT_VALUES);
464:       VecSetValuesLocal(user->eta,2,idx,vals_eta,INSERT_VALUES);
465:     }
466:     VecAssemblyBegin(user->cv);
467:     VecAssemblyEnd(user->cv);
468:     VecAssemblyBegin(user->ci);
469:     VecAssemblyEnd(user->ci);
470:     VecAssemblyBegin(user->eta);
471:     VecAssemblyEnd(user->eta);

473:     DMDARestoreElements(user->da2,&nele,&nen,&ele);
474:     VecRestoreArrayRead(coords,&_coords);


477:   } else {

479:     VecGetArray(user->cv,&cv_p);
480:     VecGetArray(user->ci,&ci_p);


483:     /* VecSet(user->cv,0.122);
484:      VecSet(user->cv,6.9e-8);
485:      VecSet(user->ci,6.9e-8); */


488:     for (i=0; i<n/5; i++) {
489:       if (i%5 <4) {
490:         cv_p[i] = 0.0;
491:         ci_p[i] = 1.0e-2;
492:       } else {
493:         cv_p[i] = 1.0e-2;
494:         ci_p[i] = 0.0;
495:       }
496:     }
497:     VecRestoreArray(user->cv,&cv_p);
498:     VecRestoreArray(user->ci,&ci_p);


501:     VecSet(user->eta,0.0);

503:   }

505:   DPsi(user);
506:   VecCopy(user->DPsiv,user->wv);
507:   VecCopy(user->DPsii,user->wi);

509:   VecGetArray(X,&xx);
510:   VecGetArray(user->cv,&cv_p);
511:   VecGetArray(user->ci,&ci_p);
512:   VecGetArray(user->eta,&eta_p);
513:   VecGetArray(user->wv,&wv_p);
514:   VecGetArray(user->wi,&wi_p);
515:   for (i=0; i<n/5; i++)
516:   {
517:     xx[5*i]   = wv_p[i];
518:     xx[5*i+1] = cv_p[i];
519:     xx[5*i+2] = wi_p[i];
520:     xx[5*i+3] = ci_p[i];
521:     xx[5*i+4] = eta_p[i];



525:   }

527:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_initial",FILE_MODE_WRITE,&view_out);
528:   VecView(user->wv,view_out);
529:   VecView(user->cv,view_out);
530:   VecView(user->wi,view_out);
531:   VecView(user->ci,view_out);
532:   VecView(user->eta,view_out);
533:   PetscViewerDestroy(&view_out);

535:   VecRestoreArray(X,&xx);
536:   VecRestoreArray(user->cv,&cv_p);
537:   VecRestoreArray(user->ci,&ci_p);
538:   VecRestoreArray(user->wv,&wv_p);
539:   VecRestoreArray(user->wi,&wi_p);   VecRestoreArray(user->eta,&eta_p);
540:   return(0);
541: }

545: PetscErrorCode SetRandomVectors(AppCtx *user)
546: {
548:   PetscInt       i,n,count=0;
549:   PetscScalar    *w1,*w2,*Pv_p,*eta_p;

551:   /* static PetscViewer viewer=0; */
552:   static PetscRandom rand = 0;
553:   static PetscInt    step = 0;

556:   if (!rand) {
557:     PetscRandomCreate(PETSC_COMM_WORLD,&rand);
558:     PetscRandomSetFromOptions(rand);
559:   }

561:   VecSetRandom(user->work1,rand);
562:   VecSetRandom(user->work2,rand);
563:   VecGetArray(user->work1,&w1);
564:   VecGetArray(user->work2,&w2);
565:   VecGetArray(user->Pv,&Pv_p);
566:   VecGetArray(user->eta,&eta_p);
567:   VecGetLocalSize(user->work1,&n);
568:   for (i=0; i<n; i++) {
569:     if (eta_p[i]>=0.8 || w1[i]>user->P_casc) Pv_p[i]=0;
570:     else {
571:       Pv_p[i]=w2[i]*user->VG;
572:       count  = count + 1;
573:     }
574:   }
575:   step++;

577:   VecCopy(user->Pv,user->Pi);
578:   VecScale(user->Pi,0.9);
579:   VecPointwiseMult(user->Piv,user->Pi,user->Pv);
580:   VecRestoreArray(user->work1,&w1);
581:   VecRestoreArray(user->work2,&w2);
582:   VecRestoreArray(user->Pv,&Pv_p);
583:   VecRestoreArray(user->eta,&eta_p);
584:   printf("Number of radiations count %d out of total mesh points n %d\n",count,n);
585:   return(0);

587: }
590: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ctx)
591: {
593:   AppCtx         *user=(AppCtx*)ctx;

596:   MatMultAdd(user->M,X,user->q,F);
597:   return(0);
598: }

602: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
603: {
605:   AppCtx         *user=(AppCtx*)ctx;

608:   MatCopy(user->M,J,*flg);
609:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
610:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
611:   return(0);
612: }
615: PetscErrorCode SetVariableBounds(DM da,Vec xl,Vec xu)
616: {
618:   PetscScalar    **l,**u;
619:   PetscInt       xs,xm;
620:   PetscInt       i;

623:   DMDAVecGetArrayDOF(da,xl,&l);
624:   DMDAVecGetArrayDOF(da,xu,&u);

626:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);


629:   for (i=xs; i < xs+xm; i++) {
630:     l[i][0] = -PETSC_INFINITY;
631:     l[i][1] = 0.0;
632:     l[i][2] = -PETSC_INFINITY;
633:     l[i][3] = 0.0;
634:     l[i][4] = 0.0;
635:     u[i][0] = PETSC_INFINITY;
636:     u[i][1] = 1.0;
637:     u[i][2] = PETSC_INFINITY;
638:     u[i][3] = 1.0;
639:     u[i][4] = 1.0;
640:   }


643:   DMDAVecRestoreArrayDOF(da,xl,&l);
644:   DMDAVecRestoreArrayDOF(da,xu,&u);
645:   return(0);
646: }

650: PetscErrorCode GetParams(AppCtx *user)
651: {
653:   PetscBool      flg;

656:   /* Set default parameters */
657:   user->xmin     = 0.0; user->xmax = 128.0;
658:   user->Dv       = 1.0; user->Di   = 1.0;
659:   user->Evf      = 0.8; user->Eif  = 0.8;
660:   user->A        = 1.0;
661:   user->kBT      = 0.11;
662:   user->kav      = 1.0;    user->kai    = 1.0; user->kaeta = 1.0;
663:   user->Rsurf    = 10.0;   user->Rbulk  = 0.0;
664:   user->L        = 10.0;   user->P_casc = 0.05;
665:   user->T        = 1.0e-2; user->dt     = 1.0e-4;
666:   user->VG       = 100.0;
667:   user->initv    = .0001;
668:   user->initeta  = 0.0;
669:   user->graphics = PETSC_TRUE;

671:   user->degenerate = PETSC_FALSE;
672:   /* void growth */
673:   user->voidgrowth = PETSC_FALSE;

675:   PetscOptionsGetReal(NULL,"-xmin",&user->xmin,&flg);
676:   PetscOptionsGetReal(NULL,"-xmax",&user->xmax,&flg);
677:   PetscOptionsGetReal(NULL,"-T",&user->T,&flg);
678:   PetscOptionsGetReal(NULL,"-dt",&user->dt,&flg);
679:   PetscOptionsBool("-degenerate","Run with degenerate mobility\n","None",user->degenerate,&user->degenerate,&flg);
680:   PetscOptionsReal("-smallnumber","Small number added to degenerate mobility\n","None",user->smallnumber,&user->smallnumber,&flg);
681:   PetscOptionsBool("-voidgrowth","Use initial conditions for void growth\n","None",user->voidgrowth,&user->voidgrowth,&flg);
682:   PetscOptionsBool("-graphics","Contour plot solutions at each timestep\n","None",user->graphics,&user->graphics,&flg);
683:   return(0);
684: }


689: PetscErrorCode SetUpMatrices(AppCtx *user)
690: {
692:   PetscInt       nele,nen,i,n;
693:   const PetscInt *ele;
694:   PetscScalar    dt=user->dt,h;

696:   PetscInt    idx[2];
697:   PetscScalar eM_0[2][2],eM_2[2][2];
698:   PetscScalar cv_sum, ci_sum;
699:   Mat         M  =user->M;
700:   Mat         M_0=user->M_0;
701:   PetscInt    Mda;
702:   PetscScalar *cv_p,*ci_p;
703:   /* newly added */
704:   Vec cvlocal,cilocal;

707:   /* new stuff */
708:   DMGetLocalVector(user->da2,&cvlocal);
709:   DMGetLocalVector(user->da2,&cilocal);
710:   DMGlobalToLocalBegin(user->da2,user->cv,INSERT_VALUES,cvlocal);
711:   DMGlobalToLocalEnd(user->da2,user->cv,INSERT_VALUES,cvlocal);
712:   DMGlobalToLocalBegin(user->da2,user->ci,INSERT_VALUES,cilocal);
713:   DMGlobalToLocalEnd(user->da2,user->ci,INSERT_VALUES,cilocal);

715:   /* old stuff */
716:   /*
717:   VecGetArray(user->cv,&cv_p);
718:   VecGetArray(user->ci,&ci_p);
719:    */
720:   /* new stuff */
721:   VecGetArray(cvlocal,&cv_p);
722:   VecGetArray(cilocal,&ci_p);

724:   MatGetLocalSize(M,&n,NULL);
725:   DMDAGetInfo(user->da1,NULL,&Mda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

727:   h = (user->xmax-user->xmin)/Mda;

729:   eM_0[0][0]=eM_0[1][1]=h/3.0;
730:   eM_0[0][1]=eM_0[1][0]=h/6.0;

732:   eM_2[0][0]=eM_2[1][1]=1.0/h;
733:   eM_2[0][1]=eM_2[1][0]=-1.0/h;

735:   /* Get local element info */
736:   DMDAGetElements(user->da1,&nele,&nen,&ele);
737:   /* for (i=0;i < nele + 1;i++) { */
738:   for (i=0; i < nele; i++) {

740:     idx[0] = ele[2*i]; idx[1] = ele[2*i+1];

742:     if (user->degenerate) {
743:       cv_sum = (2.0*user->smallnumber + cv_p[idx[0]]+cv_p[idx[1]])*user->Dv/(2.0*user->kBT);
744:       ci_sum = (2.0*user->smallnumber + ci_p[idx[0]]+ci_p[idx[1]])*user->Di/(2.0*user->kBT);
745:     } else {
746:       cv_sum = user->initv*user->Dv/user->kBT;
747:       ci_sum = user->initv*user->Di/user->kBT;
748:     }


751:     PetscInt row,cols[4],r,row_M_0,cols2[2];
752:     /* PetscScalar vals[4],vals_M_0[1],vals2[2]; */
753:     PetscScalar vals[4],vals_M_0[2],vals2[2];

755:     for (r=0; r<2; r++) {
756:       row_M_0 = idx[r];

758:       vals_M_0[0]=eM_0[r][0];
759:       vals_M_0[1]=eM_0[r][1];

761:       /* vals_M_0[0] = h; */
762:       MatSetValuesLocal(M_0,1,&row_M_0,2,idx,vals_M_0,ADD_VALUES);
763:       /* MatSetValuesLocal(M_0,1,&row_M_0,1,&row_M_0,vals_M_0,INSERT_VALUES); */

765:       row     = 5*idx[r];
766:       cols[0] = 5*idx[0];     vals[0] = dt*eM_2[r][0]*cv_sum;
767:       cols[1] = 5*idx[1];     vals[1] = dt*eM_2[r][1]*cv_sum;
768:       cols[2] = 5*idx[0]+1;   vals[2] = eM_0[r][0];
769:       cols[3] = 5*idx[1]+1;   vals[3] = eM_0[r][1];

771:       /* Insert values in matrix M for 1st dof */
772:       MatSetValuesLocal(M,1,&row,4,cols,vals,ADD_VALUES);

774:       row     = 5*idx[r]+1;
775:       cols[0] = 5*idx[0];     vals[0] = -eM_0[r][0];
776:       cols[1] = 5*idx[1];     vals[1] = -eM_0[r][1];
777:       cols[2] = 5*idx[0]+1;   vals[2] = user->kav*eM_2[r][0];
778:       cols[3] = 5*idx[1]+1;   vals[3] = user->kav*eM_2[r][1];

780:       /* Insert values in matrix M for 2nd dof */
781:       MatSetValuesLocal(M,1,&row,4,cols,vals,ADD_VALUES);

783:       row     = 5*idx[r]+2;
784:       cols[0] = 5*idx[0]+2;   vals[0] = dt*eM_2[r][0]*ci_sum;
785:       cols[1] = 5*idx[1]+2;   vals[1] = dt*eM_2[r][1]*ci_sum;
786:       cols[2] = 5*idx[0]+3;   vals[2] = eM_0[r][0];
787:       cols[3] = 5*idx[1]+3;   vals[3] = eM_0[r][1];
788:       /* Insert values in matrix M for 3nd dof */
789:       MatSetValuesLocal(M,1,&row,4,cols,vals,ADD_VALUES);

791:       row     = 5*idx[r]+3;
792:       cols[0] = 5*idx[0]+2;   vals[0] = -eM_0[r][0];
793:       cols[1] = 5*idx[1]+2;   vals[1] = -eM_0[r][1];
794:       cols[2] = 5*idx[0]+3;   vals[2] = user->kai*eM_2[r][0];
795:       cols[3] = 5*idx[1]+3;   vals[3] = user->kai*eM_2[r][1];
796:       /* Insert values in matrix M for 4th dof */
797:       MatSetValuesLocal(M,1,&row,4,cols,vals,ADD_VALUES);

799:       row      = 5*idx[r]+4;
800:       cols2[0] = 5*idx[0]+4;   vals2[0] = eM_0[r][0]/dt + user->L*user->kaeta*eM_2[r][0];
801:       cols2[1] = 5*idx[1]+4;   vals2[1] = eM_0[r][1]/dt + user->L*user->kaeta*eM_2[r][1];
802:       MatSetValuesLocal(M,1,&row,2,cols2,vals2,ADD_VALUES);
803:     }
804:   }



808:   /* new */
809:   VecRestoreArray(cvlocal,&cv_p);
810:   VecRestoreArray(cilocal,&ci_p);
811:   DMRestoreLocalVector(user->da2,&cvlocal);
812:   DMRestoreLocalVector(user->da2,&cilocal);
813:   /*
814:   VecRestoreArray(user->cv,&cv_p);
815:    VecRestoreArray(user->ci,&ci_p);*/
816:   MatAssemblyBegin(M_0,MAT_FINAL_ASSEMBLY);
817:   MatAssemblyEnd(M_0,MAT_FINAL_ASSEMBLY);

819:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
820:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);

822:   DMDARestoreElements(user->da1,&nele,&nen,&ele);
823:   return(0);
824: }


829: PetscErrorCode UpdateMatrices(AppCtx *user)
830: {
832:   PetscInt       nele,nen,i,n,Mda;
833:   const PetscInt *ele;

835:   PetscInt    idx[2];
836:   PetscScalar eM_2[2][2],h;
837:   Mat         M=user->M;
838:   PetscScalar *cv_p,*ci_p,cv_sum,ci_sum;
839:   /* newly added */
840:   Vec cvlocal,cilocal;

843:   /*new stuff */
844:   DMGetLocalVector(user->da2,&cvlocal);
845:   DMGetLocalVector(user->da2,&cilocal);
846:   DMGlobalToLocalBegin(user->da2,user->cv,INSERT_VALUES,cvlocal);
847:   DMGlobalToLocalEnd(user->da2,user->cv,INSERT_VALUES,cvlocal);
848:   DMGlobalToLocalBegin(user->da2,user->ci,INSERT_VALUES,cilocal);
849:   DMGlobalToLocalEnd(user->da2,user->ci,INSERT_VALUES,cilocal);
850:   /* old stuff */
851:   /*
852:   VecGetArray(user->cv,&cv_p);
853:   VecGetArray(user->ci,&ci_p);
854:    */

856:   /* new stuff */
857:   VecGetArray(cvlocal,&cv_p);
858:   VecGetArray(cilocal,&ci_p);

860:   /* Create the mass matrix M_0 */
861:   MatGetLocalSize(M,&n,NULL);
862:   DMDAGetInfo(user->da1,NULL,&Mda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

864:   h = (user->xmax-user->xmin)/Mda;

866:   /* Get local element info */
867:   DMDAGetElements(user->da1,&nele,&nen,&ele);

869:   for (i=0; i<nele; i++) {
870:     idx[0] = ele[2*i]; idx[1] = ele[2*i+1];

872:     PetscInt    r,row,cols[2];
873:     PetscScalar vals[2];

875:     for (r=0; r<2; r++) {
876:       row     = 5*idx[r];
877:       cols[0] = 5*idx[0];     vals[0] = 0.0;
878:       cols[1] = 5*idx[1];     vals[1] = 0.0;


881:       /* Insert values in matrix M for 1st dof */
882:       MatSetValuesLocal(M,1,&row,2,cols,vals,INSERT_VALUES);

884:       row     = 5*idx[r]+2;
885:       cols[0] = 5*idx[0]+2;   vals[0] = 0.0;
886:       cols[1] = 5*idx[1]+2;   vals[1] = 0.0;

888:       /* Insert values in matrix M for 3nd dof */
889:       MatSetValuesLocal(M,1,&row,2,cols,vals,INSERT_VALUES);
890:     }
891:   }

893:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
894:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);

896:   eM_2[0][0]=eM_2[1][1]=1.0/h;
897:   eM_2[0][1]=eM_2[1][0]=-1.0/h;

899:   for (i=0; i<nele; i++) {
900:     idx[0] = ele[2*i]; idx[1] = ele[2*i+1];

902:     PetscInt    row,cols[2],r;
903:     PetscScalar vals[2];

905:     for (r=0; r<2; r++) {

907:       if (user->degenerate) {
908:         cv_sum = (2.0*user->smallnumber + cv_p[idx[0]] + cv_p[idx[1]])*user->Dv/(2.0*user->kBT);
909:         ci_sum = (2.0*user->smallnumber + ci_p[idx[0]] + ci_p[idx[1]])*user->Di/(2.0*user->kBT);
910:       } else {
911:         cv_sum = user->initv*user->Dv/user->kBT;
912:         ci_sum = user->initv*user->Di/user->kBT;
913:       }

915:       row     = 5*idx[r];
916:       cols[0] = 5*idx[0];     vals[0] = user->dt*eM_2[r][0]*cv_sum;
917:       cols[1] = 5*idx[1];     vals[1] = user->dt*eM_2[r][1]*cv_sum;

919:       /* Insert values in matrix M for 1st dof */
920:       MatSetValuesLocal(M,1,&row,2,cols,vals,ADD_VALUES);

922:       row     = 5*idx[r]+2;
923:       cols[0] = 5*idx[0]+2;   vals[0] = user->dt*eM_2[r][0]*ci_sum;
924:       cols[1] = 5*idx[1]+2;   vals[1] = user->dt*eM_2[r][1]*ci_sum;

926:       /* Insert values in matrix M for 3nd dof */
927:       MatSetValuesLocal(M,1,&row,2,cols,vals,ADD_VALUES);
928:     }
929:   }

931:   /* old stuff
932:   VecRestoreArray(user->cv,&cv_p);
933:   VecRestoreArray(user->ci,&ci_p);
934:    */

936:   /* new stuff */
937:   VecRestoreArray(cvlocal,&cv_p);
938:   VecRestoreArray(cilocal,&ci_p);
939:   DMRestoreLocalVector(user->da2,&cvlocal);
940:   DMRestoreLocalVector(user->da2,&cilocal);

942:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
943:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);
944:   DMDARestoreElements(user->da1,&nele,&nen,&ele);
945:   return(0);
946: }


951: PetscErrorCode CheckRedundancy(SNES snes, IS act, IS *outact, DM da)
952: {
954:   PetscScalar    **uin,**uout;
955:   Vec            UIN, UOUT;
956:   PetscInt       xs,xm,*outindex;
957:   const PetscInt *index;
958:   PetscInt       k,i,l,n,M,cnt=0;

961:   DMDAGetInfo(da,0,&M,0,0,0,0,0,0,0,0,0,0,0);
962:   DMGetGlobalVector(da,&UIN);
963:   VecSet(UIN,0.0);
964:   DMGetLocalVector(da,&UOUT);
965:   DMDAVecGetArrayDOF(da,UIN,&uin);
966:   ISGetIndices(act,&index);
967:   ISGetLocalSize(act,&n);
968:   for (k=0; k<n; k++) {
969:     l        = index[k]%5;
970:     i        = index[k]/5;
971:     uin[i][l]=1.0;
972:   }
973:   printf("Number of active constraints before applying redundancy %d\n",n);
974:   ISRestoreIndices(act,&index);
975:   DMDAVecRestoreArrayDOF(da,UIN,&uin);
976:   DMGlobalToLocalBegin(da,UIN,INSERT_VALUES,UOUT);
977:   DMGlobalToLocalEnd(da,UIN,INSERT_VALUES,UOUT);
978:   DMDAVecGetArrayDOF(da,UOUT,&uout);

980:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

982:   for (i=xs; i < xs+xm; i++) {
983:     if (uout[i-1][1] && uout[i][1] && uout[i+1][1]) uout[i][0] = 1.0;
984:     if (uout[i-1][3] && uout[i][3] && uout[i+1][3]) uout[i][2] = 1.0;
985:   }

987:   for (i=xs; i < xs+xm; i++) {
988:     for (l=0; l < 5; l++) {
989:       if (uout[i][l]) cnt++;
990:     }
991:   }

993:   printf("Number of active constraints after applying redundancy %d\n",cnt);


996:   PetscMalloc1(cnt,&outindex);
997:   cnt  = 0;

999:   for (i=xs; i < xs+xm; i++) {
1000:     for (l=0; l < 5; l++) {
1001:       if (uout[i][l]) outindex[cnt++] = 5*(i)+l;
1002:     }
1003:   }


1006:   ISCreateGeneral(PETSC_COMM_WORLD,cnt,outindex,PETSC_OWN_POINTER,outact);
1007:   DMDAVecRestoreArrayDOF(da,UOUT,&uout);
1008:   DMRestoreGlobalVector(da,&UIN);
1009:   DMRestoreLocalVector(da,&UOUT);
1010:   return(0);
1011: }