Actual source code: ex63.c

petsc-3.4.4 2014-03-13
  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*,MatStructure*,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,DMDA_BOUNDARY_PERIODIC, -4, 5, 1,NULL,&user.da1);
 71:   DMDACreate1d(PETSC_COMM_WORLD,DMDA_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,DMDA_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:   DMCreateMatrix(user.da1,MATAIJ,&user.M);
113:   /* Get the (usual) mass matrix structure from da2 */
114:   DMCreateMatrix(user.da2,MATAIJ,&user.M_0);
115:   SetInitialGuess(x,&user);
116:   /* Form the jacobian matrix and M_0 */
117:   SetUpMatrices(&user);
118:   MatDuplicate(user.M,MAT_DO_NOT_COPY_VALUES,&J);

120:   SNESCreate(PETSC_COMM_WORLD,&snes);
121:   SNESSetDM(snes,user.da1);

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

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

137:   if (user.graphics) {
138:     PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),5,bounds);

140:     VecView(x,PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD));
141:   }
142:   while (t<user.T) {
143:     char        filename[PETSC_MAX_PATH_LEN];
144:     PetscScalar a = 1.0;
145:     PetscInt    i;
146:     PetscViewer view;


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

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

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

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

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

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

187:   }


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

232: PetscErrorCode Update_u(Vec X,AppCtx *user)
233: {
235:   PetscInt       i,n;
236:   PetscScalar    *xx,*wv_p,*cv_p,*wi_p,*ci_p,*eta_p;
237:   PetscInt       pv1,pi1,peta1,pv2,pi2,peta2;
238:   PetscReal      maxv,maxi,maxeta,minv,mini,mineta;


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


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


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


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

279: PetscErrorCode Update_q(AppCtx *user)
280: {
282:   PetscScalar    *q_p, *w1, *w2;
283:   PetscInt       i,n;
284:   PetscScalar    norm1;

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

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

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

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

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

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

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

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

330: PetscErrorCode DPsi(AppCtx *user)
331: {
333:   PetscScalar    Evf=user->Evf,Eif=user->Eif,kBT=user->kBT,A=user->A;
334:   PetscScalar    *cv_p,*ci_p,*eta_p,*logcv_p,*logci_p,*logcvi_p,*DPsiv_p,*DPsii_p,*DPsieta_p;
335:   PetscInt       n,i;

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

349:   Llog(user->cv,user->logcv);
350:   Llog(user->ci,user->logci);

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

358:   for (i=0; i<n; i++)
359:   {
360:     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);
361:     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];

363:     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]);
364:   }

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

377: }


382: PetscErrorCode Llog(Vec X, Vec Y)
383: {
385:   PetscScalar    *x,*y;
386:   PetscInt       n,i;

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

401: PetscErrorCode SetInitialGuess(Vec X,AppCtx *user)
402: {

405:   PetscInt          n,i,Mda;
406:   PetscScalar       *xx,*cv_p,*ci_p,*wv_p,*wi_p,*eta_p;
407:   PetscViewer       view_out;
408:   /* needed for the void growth case */
409:   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;
410:   PetscInt          nele,nen,idx[2];
411:   const PetscInt    *ele;
412:   PetscScalar       x[2];
413:   Vec               coords;
414:   const PetscScalar *_coords;
415:   PetscViewer       view;
416:   PetscScalar       xwidth = user->xmax - user->xmin;

419:   VecGetLocalSize(X,&n);

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

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

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

434:       x[0] = _coords[idx[0]];
435:       x[1] = _coords[idx[1]];


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

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

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


475:   } else {

477:     VecGetArray(user->cv,&cv_p);
478:     VecGetArray(user->ci,&ci_p);


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


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


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

501:   }

503:   DPsi(user);
504:   VecCopy(user->DPsiv,user->wv);
505:   VecCopy(user->DPsii,user->wi);

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



523:   }

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

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

543: PetscErrorCode SetRandomVectors(AppCtx *user)
544: {
546:   PetscInt       i,n,count=0;
547:   PetscScalar    *w1,*w2,*Pv_p,*eta_p;

549:   /* static PetscViewer viewer=0; */
550:   static PetscRandom rand = 0;
551:   static PetscInt    step = 0;

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

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

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

585: }
588: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ctx)
589: {
591:   AppCtx         *user=(AppCtx*)ctx;

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

600: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *flg,void *ctx)
601: {
603:   AppCtx         *user=(AppCtx*)ctx;

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

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

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


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


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

649: PetscErrorCode GetParams(AppCtx *user)
650: {
652:   PetscBool      flg;

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

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

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


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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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



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

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

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


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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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


995:   PetscMalloc(cnt*sizeof(PetscInt),&outindex);
996:   cnt  = 0;

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


1005:   ISCreateGeneral(PETSC_COMM_WORLD,cnt,outindex,PETSC_OWN_POINTER,outact);
1006:   DMDAVecRestoreArrayDOF(da,UOUT,&uout);
1007:   DMRestoreGlobalVector(da,&UIN);
1008:   DMRestoreLocalVector(da,&UOUT);
1009:   return(0);
1010: }