Actual source code: ex60.c

petsc-3.5.1 2014-08-06
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  1: static char help[] = "2D coupled Allen-Cahn and Cahn-Hilliard equation for constant 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:  ./ex60 -ksp_type fgmres -pc_type mg  -snes_vi_monitor   -snes_atol 1.e-11  -da_grid_x 72 -da_grid_y 72 -ksp_rtol 1.e-8  -T 0.1  -VG 100 -pc_type lu -ksp_monitor_true_residual -pc_factor_mat_solver_package superlu -snes_converged_reason -ksp_converged_reason -pc_type sor  -ksp_rtol 1.e-9  -snes_linesearch_monitor -VG 10 -draw_fields 1,3,4 -snes_monitor_solution

 14:  */

 16: /*
 17:    Possible additions to the code. At each iteration count the number of solution elements that are at the upper bound and stop the program if large

 19:    Add command-line option for constant or degenerate mobility
 20:    Add command-line option for graphics at each time step

 22:    Check time-step business; what should it be? How to check that it is good?
 23:    Make random right hand side forcing function proportional to time step so smaller time steps don't mean more radiation
 24:    How does the multigrid linear solver work now?
 25:    What happens when running with degenerate mobility


 28:  */

 30: #include <petscsnes.h>
 31: #include <petscdmda.h>

 33: typedef struct {
 34:   PetscReal   dt,T; /* Time step and end time */
 35:   DM          da1,da2;
 36:   Mat         M;    /* Jacobian matrix */
 37:   Mat         M_0;
 38:   Vec         q,wv,cv,wi,ci,eta,cvi,DPsiv,DPsii,DPsieta,Pv,Pi,Piv,logcv,logci,logcvi,Rr,Riv;
 39:   Vec         work1,work2,work3,work4;
 40:   PetscScalar Dv,Di,Evf,Eif,A,kBT,kav,kai,kaeta,Rsurf,Rbulk,L,P_casc,VG; /* physics parameters */
 41:   PetscReal   xmin,xmax,ymin,ymax;
 42:   PetscInt    Mda, Nda;
 43: } AppCtx;

 45: PetscErrorCode GetParams(AppCtx*);
 46: PetscErrorCode SetRandomVectors(AppCtx*);
 47: PetscErrorCode SetVariableBounds(DM,Vec,Vec);
 48: PetscErrorCode SetUpMatrices(AppCtx*);
 49: PetscErrorCode UpdateMatrices(AppCtx*);
 50: PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
 51: PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);
 52: PetscErrorCode SetInitialGuess(Vec,AppCtx*);
 53: PetscErrorCode Update_q(AppCtx*);
 54: PetscErrorCode Update_u(Vec,AppCtx*);
 55: PetscErrorCode DPsi(AppCtx*);
 56: PetscErrorCode LaplacianFiniteDifference(AppCtx*);
 57: PetscErrorCode Llog(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:   AppCtx         user; /* Application context */
 66:   Vec            xl,xu; /* Upper and lower bounds on variables */
 67:   Mat            J;
 68:   PetscScalar    t=0.0;
 69:   PetscViewer    view_out, view_q, view_psi, view_mat;
 70:   PetscViewer    view_rand;
 71:   IS             inactiveconstraints;
 72:   PetscInt       ninactiveconstraints,N;

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

 76:   /* Get physics and time parameters */
 77:   GetParams(&user);
 78:   /* Create a 1D DA with dof = 5; the whole thing */
 79:   DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX, -3,-3,PETSC_DECIDE,PETSC_DECIDE, 5, 1,NULL,NULL,&user.da1);

 81:   /* Create a 1D DA with dof = 1; for individual componentes */
 82:   DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX, -3,-3,PETSC_DECIDE,PETSC_DECIDE, 1, 1,NULL,NULL,&user.da2);


 85:   /* Set Element type (triangular) */
 86:   DMDASetElementType(user.da1,DMDA_ELEMENT_P1);
 87:   DMDASetElementType(user.da2,DMDA_ELEMENT_P1);

 89:   /* Set x and y coordinates */
 90:   DMDASetUniformCoordinates(user.da1,user.xmin,user.xmax,user.ymin,user.ymax,NULL,NULL);
 91:   DMDASetUniformCoordinates(user.da2,user.xmin,user.xmax,user.ymin,user.ymax,NULL,NULL);
 92:   /* Get global vector x from DM (da1) and duplicate vectors r,xl,xu */
 93:   DMCreateGlobalVector(user.da1,&x);
 94:   VecGetSize(x,&N);
 95:   VecDuplicate(x,&r);
 96:   VecDuplicate(x,&xl);
 97:   VecDuplicate(x,&xu);
 98:   VecDuplicate(x,&user.q);

100:   /* Get global vector user->wv from da2 and duplicate other vectors */
101:   DMCreateGlobalVector(user.da2,&user.wv);
102:   VecDuplicate(user.wv,&user.cv);
103:   VecDuplicate(user.wv,&user.wi);
104:   VecDuplicate(user.wv,&user.ci);
105:   VecDuplicate(user.wv,&user.eta);
106:   VecDuplicate(user.wv,&user.cvi);
107:   VecDuplicate(user.wv,&user.DPsiv);
108:   VecDuplicate(user.wv,&user.DPsii);
109:   VecDuplicate(user.wv,&user.DPsieta);
110:   VecDuplicate(user.wv,&user.Pv);
111:   VecDuplicate(user.wv,&user.Pi);
112:   VecDuplicate(user.wv,&user.Piv);
113:   VecDuplicate(user.wv,&user.logcv);
114:   VecDuplicate(user.wv,&user.logci);
115:   VecDuplicate(user.wv,&user.logcvi);
116:   VecDuplicate(user.wv,&user.work1);
117:   VecDuplicate(user.wv,&user.work2);
118:   VecDuplicate(user.wv,&user.Rr);
119:   VecDuplicate(user.wv,&user.Riv);


122:   /* Get Jacobian matrix structure from the da for the entire thing, da1 */
123:   DMSetMatType(user.da1,MATAIJ);
124:   DMCreateMatrix(user.da1,&user.M);
125:   /* Get the (usual) mass matrix structure from da2 */
126:   DMSetMatType(user.da2,MATAIJ);
127:   DMCreateMatrix(user.da2,&user.M_0);
128:   SetInitialGuess(x,&user);
129:   /* Form the jacobian matrix and M_0 */
130:   SetUpMatrices(&user);
131:   MatDuplicate(user.M,MAT_DO_NOT_COPY_VALUES,&J);

133:   SNESCreate(PETSC_COMM_WORLD,&snes);
134:   SNESSetDM(snes,user.da1);

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

139:   SetVariableBounds(user.da1,xl,xu);
140:   SNESVISetVariableBounds(snes,xl,xu);
141:   SNESSetFromOptions(snes);

143:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_rand",FILE_MODE_WRITE,&view_rand);
144:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_mat",FILE_MODE_WRITE,&view_mat);
145:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_q",FILE_MODE_WRITE,&view_q);
146:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_out",FILE_MODE_WRITE,&view_out);
147:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_psi",FILE_MODE_WRITE,&view_psi);

149:   while (t<user.T) {
150:     SNESSetFunction(snes,r,FormFunction,(void*)&user);
151:     SNESSetJacobian(snes,J,J,FormJacobian,(void*)&user);

153:     SetRandomVectors(&user);
154:     /*    VecView(user.Pv,view_rand);
155:     VecView(user.Pi,view_rand);
156:      VecView(user.Piv,view_rand);*/

158:     DPsi(&user);
159:     /*    VecView(user.DPsiv,view_psi);
160:     VecView(user.DPsii,view_psi);
161:      VecView(user.DPsieta,view_psi);*/

163:     Update_q(&user);
164:     /*    VecView(user.q,view_q);
165:      MatView(user.M,view_mat);*/
166:     SNESSolve(snes,NULL,x);
167:     SNESVIGetInactiveSet(snes,&inactiveconstraints);
168:     ISGetSize(inactiveconstraints,&ninactiveconstraints);
169:     /* if (ninactiveconstraints < .90*N) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP,"To many active constraints, model has become non-physical"); */

171:     /*    VecView(x,view_out);*/
172:     VecView(x,PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD));
173:     PetscInt its;
174:     SNESGetIterationNumber(snes,&its);
175:     PetscPrintf(PETSC_COMM_WORLD,"SNESVI solver converged at t = %5.4f in %d iterations\n",t,its);

177:     Update_u(x,&user);
178:     UpdateMatrices(&user);
179:     t    = t + user.dt;
180:   }

182:   PetscViewerDestroy(&view_rand);
183:   PetscViewerDestroy(&view_mat);
184:   PetscViewerDestroy(&view_q);
185:   PetscViewerDestroy(&view_out);
186:   PetscViewerDestroy(&view_psi);

188:   VecDestroy(&x);
189:   VecDestroy(&r);
190:   VecDestroy(&xl);
191:   VecDestroy(&xu);
192:   VecDestroy(&user.q);
193:   VecDestroy(&user.wv);
194:   VecDestroy(&user.cv);
195:   VecDestroy(&user.wi);
196:   VecDestroy(&user.ci);
197:   VecDestroy(&user.eta);
198:   VecDestroy(&user.cvi);
199:   VecDestroy(&user.DPsiv);
200:   VecDestroy(&user.DPsii);
201:   VecDestroy(&user.DPsieta);
202:   VecDestroy(&user.Pv);
203:   VecDestroy(&user.Pi);
204:   VecDestroy(&user.Piv);
205:   VecDestroy(&user.logcv);
206:   VecDestroy(&user.logci);
207:   VecDestroy(&user.logcvi);
208:   VecDestroy(&user.work1);
209:   VecDestroy(&user.work2);
210:   VecDestroy(&user.Rr);
211:   VecDestroy(&user.Riv);
212:   MatDestroy(&user.M);
213:   MatDestroy(&user.M_0);
214:   DMDestroy(&user.da1);
215:   DMDestroy(&user.da2);

217:   PetscFinalize();
218:   return 0;
219: }

223: PetscErrorCode Update_u(Vec X,AppCtx *user)
224: {
226:   PetscInt       i,n;
227:   PetscScalar    *xx,*wv_p,*cv_p,*wi_p,*ci_p,*eta_p;

230:   VecGetLocalSize(user->wv,&n);
231:   VecGetArray(X,&xx);
232:   VecGetArray(user->wv,&wv_p);
233:   VecGetArray(user->cv,&cv_p);
234:   VecGetArray(user->wi,&wi_p);
235:   VecGetArray(user->ci,&ci_p);
236:   VecGetArray(user->eta,&eta_p);


239:   for (i=0; i<n; i++) {
240:     wv_p[i]  = xx[5*i];
241:     cv_p[i]  = xx[5*i+1];
242:     wi_p[i]  = xx[5*i+2];
243:     ci_p[i]  = xx[5*i+3];
244:     eta_p[i] = xx[5*i+4];
245:   }
246:   VecRestoreArray(X,&xx);
247:   VecRestoreArray(user->wv,&wv_p);
248:   VecRestoreArray(user->cv,&cv_p);
249:   VecRestoreArray(user->wi,&wi_p);
250:   VecRestoreArray(user->ci,&ci_p);
251:   VecRestoreArray(user->eta,&eta_p);
252:   return(0);
253: }

257: PetscErrorCode Update_q(AppCtx *user)
258: {
260:   PetscScalar    *q_p,*w1,*w2;
261:   PetscInt       i,n;

264:   VecPointwiseMult(user->Rr,user->eta,user->eta);
265:   VecScale(user->Rr,user->Rsurf);
266:   VecShift(user->Rr,user->Rbulk);
267:   VecPointwiseMult(user->Riv,user->cv,user->ci);
268:   VecPointwiseMult(user->Riv,user->Rr,user->Riv);

270:   VecGetArray(user->q,&q_p);
271:   VecGetArray(user->work1,&w1);
272:   VecGetArray(user->work2,&w2);

274:   VecCopy(user->cv,user->work1);
275:   VecAXPY(user->work1,1.0,user->Pv);
276:   VecScale(user->work1,-1.0);
277:   MatMult(user->M_0,user->work1,user->work2);
278:   VecGetLocalSize(user->work1,&n);

280:   for (i=0; i<n; i++) q_p[5*i]=w2[i];

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

285:   VecCopy(user->ci,user->work1);
286:   VecAXPY(user->work1,1.0,user->Pi);
287:   VecScale(user->work1,-1.0);
288:   MatMult(user->M_0,user->work1,user->work2);
289:   for (i=0; i<n; i++) q_p[5*i+2]=w2[i];

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

294:   VecCopy(user->eta,user->work1);
295:   VecScale(user->work1,-1.0/user->dt);
296:   VecAXPY(user->work1,user->L,user->DPsieta);
297:   VecAXPY(user->work1,-1.0,user->Piv);
298:   MatMult(user->M_0,user->work1,user->work2);
299:   for (i=0; i<n; i++) q_p[5*i+4]=w2[i];

301:   VecRestoreArray(user->q,&q_p);
302:   VecRestoreArray(user->work1,&w1);
303:   VecRestoreArray(user->work2,&w2);
304:   return(0);
305: }

309: PetscErrorCode DPsi(AppCtx *user)
310: {
312:   PetscScalar    Evf=user->Evf,Eif=user->Eif,kBT=user->kBT,A=user->A;
313:   PetscScalar    *cv_p,*ci_p,*eta_p,*logcv_p,*logci_p,*logcvi_p,*DPsiv_p,*DPsii_p,*DPsieta_p;
314:   PetscInt       n,i;

317:   VecGetLocalSize(user->cv,&n);
318:   VecGetArray(user->cv,&cv_p);
319:   VecGetArray(user->ci,&ci_p);
320:   VecGetArray(user->eta,&eta_p);
321:   VecGetArray(user->logcv,&logcv_p);
322:   VecGetArray(user->logci,&logci_p);
323:   VecGetArray(user->logcvi,&logcvi_p);
324:   VecGetArray(user->DPsiv,&DPsiv_p);
325:   VecGetArray(user->DPsii,&DPsii_p);
326:   VecGetArray(user->DPsieta,&DPsieta_p);

328:   Llog(user->cv,user->logcv);

330:   Llog(user->ci,user->logci);


333:   VecCopy(user->cv,user->cvi);
334:   VecAXPY(user->cvi,1.0,user->ci);
335:   VecScale(user->cvi,-1.0);
336:   VecShift(user->cvi,1.0);
337:   Llog(user->cvi,user->logcvi);

339:   for (i=0; i<n; i++)
340:   {
341:     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);
342:     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];

344:     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]);
345:   }

347:   VecRestoreArray(user->cv,&cv_p);
348:   VecRestoreArray(user->ci,&ci_p);
349:   VecRestoreArray(user->eta,&eta_p);
350:   VecRestoreArray(user->logcv,&logcv_p);
351:   VecRestoreArray(user->logci,&logci_p);
352:   VecRestoreArray(user->logcvi,&logcvi_p);
353:   VecRestoreArray(user->DPsiv,&DPsiv_p);
354:   VecRestoreArray(user->DPsii,&DPsii_p);
355:   VecRestoreArray(user->DPsieta,&DPsieta_p);
356:   return(0);
357: }


362: PetscErrorCode Llog(Vec X, Vec Y)
363: {
365:   PetscScalar    *x,*y;
366:   PetscInt       n,i;

369:   VecGetArray(X,&x);
370:   VecGetArray(Y,&y);
371:   VecGetLocalSize(X,&n);
372:   for (i=0; i<n; i++) {
373:     if (x[i] < 1.0e-12) y[i] = log(1.0e-12);
374:     else y[i] = log(x[i]);
375:   }
376:   return(0);
377: }


382: PetscErrorCode SetInitialGuess(Vec X,AppCtx *user)
383: {
385:   PetscInt       n,i;
386:   PetscScalar    *xx,*cv_p,*ci_p,*wv_p,*wi_p;
387:   PetscViewer    view;
388:   PetscScalar    initv = .00069;

391:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_initial",FILE_MODE_WRITE,&view);
392:   VecGetLocalSize(X,&n);

394:   VecSet(user->cv,initv);
395:   VecSet(user->ci,initv);
396:   VecSet(user->eta,0.0);

398:   DPsi(user);
399:   VecCopy(user->DPsiv,user->wv);
400:   VecCopy(user->DPsii,user->wi);

402:   VecGetArray(X,&xx);
403:   VecGetArray(user->cv,&cv_p);
404:   VecGetArray(user->ci,&ci_p);
405:   VecGetArray(user->wv,&wv_p);
406:   VecGetArray(user->wi,&wi_p);
407:   for (i=0; i<n/5; i++) {
408:     xx[5*i]  =wv_p[i];
409:     xx[5*i+1]=cv_p[i];
410:     xx[5*i+2]=wi_p[i];
411:     xx[5*i+3]=ci_p[i];
412:     xx[5*i+4]=0.0;
413:   }

415:   VecView(user->wv,view);
416:   VecView(user->cv,view);
417:   VecView(user->wi,view);
418:   VecView(user->ci,view);
419:   PetscViewerDestroy(&view);

421:   VecRestoreArray(X,&xx);
422:   VecRestoreArray(user->cv,&cv_p);
423:   VecRestoreArray(user->ci,&ci_p);
424:   VecRestoreArray(user->wv,&wv_p);
425:   VecRestoreArray(user->wi,&wi_p);
426:   return(0);
427: }

431: PetscErrorCode SetRandomVectors(AppCtx *user)
432: {
434:   PetscInt       i,n,count=0;
435:   PetscScalar    *w1,*w2,*Pv_p,*eta_p;

438:   VecSetRandom(user->work1,NULL);
439:   VecSetRandom(user->work2,NULL);
440:   VecGetArray(user->work1,&w1);
441:   VecGetArray(user->work2,&w2);
442:   VecGetArray(user->Pv,&Pv_p);
443:   VecGetArray(user->eta,&eta_p);
444:   VecGetLocalSize(user->work1,&n);
445:   for (i=0; i<n; i++) {

447:     if (eta_p[i]>=0.8 || w1[i]>user->P_casc) Pv_p[i]=0;
448:     else {
449:       Pv_p[i]=w2[i]*user->VG;
450:       count  =count+1;
451:     }

453:   }

455:   VecCopy(user->Pv,user->Pi);
456:   VecScale(user->Pi,0.9);
457:   VecPointwiseMult(user->Piv,user->Pi,user->Pv);
458:   VecRestoreArray(user->work1,&w1);
459:   VecRestoreArray(user->work2,&w2);
460:   VecRestoreArray(user->Pv,&Pv_p);
461:   VecRestoreArray(user->eta,&eta_p);
462:   return(0);

464: }

468: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ctx)
469: {
471:   AppCtx         *user=(AppCtx*)ctx;

474:   MatMultAdd(user->M,X,user->q,F);
475:   return(0);
476: }

480: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
481: {
483:   AppCtx         *user=(AppCtx*)ctx;

486:   MatCopy(user->M,J,*flg);
487:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
488:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
489:   return(0);
490: }
493: PetscErrorCode SetVariableBounds(DM da,Vec xl,Vec xu)
494: {
496:   PetscScalar    ***l,***u;
497:   PetscInt       xs,xm,ys,ym;
498:   PetscInt       j,i;

501:   DMDAVecGetArrayDOF(da,xl,&l);
502:   DMDAVecGetArrayDOF(da,xu,&u);

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

506:   for (j=ys; j<ys+ym; j++) {
507:     for (i=xs; i < xs+xm; i++) {
508:       l[j][i][0] = -PETSC_INFINITY;
509:       l[j][i][1] = 0.0;
510:       l[j][i][2] = -PETSC_INFINITY;
511:       l[j][i][3] = 0.0;
512:       l[j][i][4] = 0.0;
513:       u[j][i][0] = PETSC_INFINITY;
514:       u[j][i][1] = 1.0;
515:       u[j][i][2] = PETSC_INFINITY;
516:       u[j][i][3] = 1.0;
517:       u[j][i][4] = 1.0;
518:     }
519:   }


522:   DMDAVecRestoreArrayDOF(da,xl,&l);
523:   DMDAVecRestoreArrayDOF(da,xu,&u);
524:   return(0);
525: }

529: PetscErrorCode GetParams(AppCtx *user)
530: {
532:   PetscBool      flg;

535:   /* Set default parameters */
536:   user->xmin  = 0.0; user->xmax = 1.0;
537:   user->ymin  = 0.0; user->ymax = 1.0;
538:   user->Dv    = 1.0; user->Di=4.0;
539:   user->Evf   = 0.8; user->Eif = 1.2;
540:   user->A     = 1.0;
541:   user->kBT   = 0.11;
542:   user->kav   = 1.0; user->kai = 1.0; user->kaeta = 1.0;
543:   user->Rsurf = 10.0; user->Rbulk = 1.0;
544:   user->L     = 10.0; user->P_casc = 0.05;
545:   user->T     = 1.0e-2;    user->dt = 1.0e-4;
546:   user->VG    = 100.0;

548:   PetscOptionsGetReal(NULL,"-xmin",&user->xmin,&flg);
549:   PetscOptionsGetReal(NULL,"-xmax",&user->xmax,&flg);
550:   PetscOptionsGetReal(NULL,"-T",&user->T,&flg);
551:   PetscOptionsGetReal(NULL,"-dt",&user->dt,&flg);
552:   PetscOptionsGetReal(NULL,"-P_casc",&user->P_casc,&flg);
553:   PetscOptionsGetReal(NULL,"-VG",&user->VG,&flg);
554:   return(0);
555: }


560: PetscErrorCode SetUpMatrices(AppCtx *user)
561: {
563:   PetscInt       nele,nen,i,j,n;
564:   const PetscInt *ele;
565:   PetscScalar    dt=user->dt,hx,hy;

567:   PetscInt    idx[3],*nodes, *connect, k;
568:   PetscScalar eM_0[3][3],eM_2_even[3][3],eM_2_odd[3][3];
569:   PetscScalar cv_sum, ci_sum;
570:   Mat         M  =user->M;
571:   Mat         M_0=user->M_0;
572:   PetscInt    Mda=user->Mda, Nda=user->Nda, ld, rd, ru, lu;
573:   PetscScalar *cv_p,*ci_p;

576:   /*  MatSetOption(M,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
577:    MatSetOption(M_0,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);*/

579:   /* Create the mass matrix M_0 */
580:   VecGetArray(user->cv,&cv_p);
581:   VecGetArray(user->ci,&ci_p);
582:   MatGetLocalSize(M,&n,NULL);
583:   DMDAGetInfo(user->da1,NULL,&Mda,&Nda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

585:   PetscMalloc1((Mda+1)*(Nda+1),&nodes);
586:   PetscMalloc1(Mda*Nda*2*3,&connect);
587:   hx   = (user->xmax-user->xmin)/Mda;
588:   hy   = (user->ymax-user->ymin)/Nda;
589:   for (j=0; j < Nda; j++) {
590:     for (i=0; i < Mda; i++) nodes[j*(Mda+1)+i] = j*Mda+i;
591:     nodes[j*(Mda+1)+Mda] = j*Mda;
592:   }

594:   for (i=0; i < Mda; i++) nodes[Nda*(Mda+1)+i] = i;

596:   nodes[Nda*(Mda+1)+Mda] = 0;

598:   k = 0;
599:   for (j=0; j<Nda; j++) {
600:     for (i=0; i<Mda; i++) {

602:       /* ld = nodes[j][i]; */
603:       ld = nodes[j*(Mda+1)+i];
604:       /* rd = nodes[j+1][i]; */
605:       rd = nodes[(j+1)*(Mda+1)+i];
606:       /* ru = nodes[j+1][i+1]; */
607:       ru = nodes[(j+1)*(Mda+1)+i+1];
608:       /* lu = nodes[j][i+1]; */
609:       lu = nodes[j*(Mda+1)+i+1];

611:       /* connect[k][0]=ld; */
612:       connect[k*6]=ld;
613:       /* connect[k][1]=lu; */
614:       connect[k*6+1]=lu;
615:       /* connect[k][2]=ru; */
616:       connect[k*6+2]=rd;
617:       connect[k*6+3]=lu;
618:       connect[k*6+4]=ru;
619:       connect[k*6+5]=rd;

621:       k = k+1;
622:     }
623:   }


626:   eM_0[0][0]=eM_0[1][1]=eM_0[2][2]=hx*hy/12.0;
627:   eM_0[0][1]=eM_0[0][2]=eM_0[1][0]=eM_0[1][2]=eM_0[2][0]=eM_0[2][1]=hx*hy/24.0;

629:   eM_2_odd[0][0] = 1.0;
630:   eM_2_odd[1][1] = eM_2_odd[2][2] = 0.5;
631:   eM_2_odd[0][1] = eM_2_odd[0][2] = eM_2_odd[1][0]= eM_2_odd[2][0] = -0.5;
632:   eM_2_odd[1][2] = eM_2_odd[2][1] = 0.0;

634:   eM_2_even[1][1] = 1.0;
635:   eM_2_even[0][0] = eM_2_even[2][2] = 0.5;
636:   eM_2_even[0][1] = eM_2_even[1][0] = eM_2_even[1][2] = eM_2_even[2][1] = -0.5;
637:   eM_2_even[0][2] = eM_2_even[2][0] = 0.0;


640:   for (k=0; k < Mda*Nda*2; k++) {
641:     idx[0] = connect[k*3];
642:     idx[1] = connect[k*3+1];
643:     idx[2] = connect[k*3+2];

645:     PetscInt    row,cols[6],r,row_M_0,cols3[3];
646:     PetscScalar vals[6],vals_M_0[3],vals3[3];

648:     for (r=0; r<3; r++) {
649:       row_M_0 = connect[k*3+r];

651:       vals_M_0[0]=eM_0[r][0];
652:       vals_M_0[1]=eM_0[r][1];
653:       vals_M_0[2]=eM_0[r][2];


656:       MatSetValues(M_0,1,&row_M_0,3,idx,vals_M_0,ADD_VALUES);

658:       /* cv_sum = (cv_p[idx[0]] + cv_p[idx[1]] + cv_p[idx[2]])*user->Dv/(3.0*user->kBT); */
659:       /* ci_sum = (ci_p[idx[0]] + ci_p[idx[1]] + ci_p[idx[2]])*user->Di/(3.0*user->kBT); */
660:       cv_sum = .0000069*user->Dv/user->kBT;
661:       ci_sum = .0000069*user->Di/user->kBT;

663:       if (k%2 == 0) {
664:         row     = 5*idx[r];
665:         cols[0] = 5*idx[0];     vals[0] = dt*eM_2_odd[r][0]*cv_sum;
666:         cols[1] = 5*idx[1];     vals[1] = dt*eM_2_odd[r][1]*cv_sum;
667:         cols[2] = 5*idx[2];     vals[2] = dt*eM_2_odd[r][2]*cv_sum;
668:         cols[3] = 5*idx[0]+1;   vals[3] = eM_0[r][0];
669:         cols[4] = 5*idx[1]+1;   vals[4] = eM_0[r][1];
670:         cols[5] = 5*idx[2]+1;   vals[5] = eM_0[r][2];

672:         MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);

674:         row     = 5*idx[r]+1;
675:         cols[0] = 5*idx[0];     vals[0] = -1.0*eM_0[r][0];
676:         cols[1] = 5*idx[1];     vals[1] = -1.0*eM_0[r][1];
677:         cols[2] = 5*idx[2];     vals[2] = -1.0*eM_0[r][2];
678:         cols[3] = 5*idx[0]+1;   vals[3] =  user->kav*eM_2_odd[r][0];
679:         cols[4] = 5*idx[1]+1;   vals[4] =  user->kav*eM_2_odd[r][1];
680:         cols[5] = 5*idx[2]+1;   vals[5] =  user->kav*eM_2_odd[r][2];

682:         MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);

684:         row     = 5*idx[r]+2;
685:         cols[0] = 5*idx[0]+2;   vals[0] =  dt*eM_2_odd[r][0]*ci_sum;
686:         cols[1] = 5*idx[1]+2;   vals[1] =  dt*eM_2_odd[r][1]*ci_sum;
687:         cols[2] = 5*idx[2]+2;   vals[2] =  dt*eM_2_odd[r][2]*ci_sum;
688:         cols[3] = 5*idx[0]+3;   vals[3] =  eM_0[r][0];
689:         cols[4] = 5*idx[1]+3;   vals[4] =  eM_0[r][1];
690:         cols[5] = 5*idx[2]+3;   vals[5] =  eM_0[r][2];

692:         MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);

694:         row     = 5*idx[r]+3;
695:         cols[0] = 5*idx[0]+2;   vals[0] = -1.0*eM_0[r][0];
696:         cols[1] = 5*idx[1]+2;   vals[1] = -1.0*eM_0[r][1];
697:         cols[2] = 5*idx[2]+2;   vals[2] = -1.0*eM_0[r][2];
698:         cols[3] = 5*idx[0]+3;   vals[3] =  user->kai*eM_2_odd[r][0];
699:         cols[4] = 5*idx[1]+3;   vals[4] =  user->kai*eM_2_odd[r][1];
700:         cols[5] = 5*idx[2]+3;   vals[5] =  user->kai*eM_2_odd[r][2];

702:         MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);

704:         row = 5*idx[r]+4;
705:         /*
706:         cols3[0] = 5*idx[0]+4;   vals3[0] = eM_0[r][0]/dt + user->L*user->kaeta*dt*eM_2_odd[r][0];
707:         cols3[1] = 5*idx[1]+4;   vals3[1] = eM_0[r][1]/dt + user->L*user->kaeta*dt*eM_2_odd[r][1];
708:         cols3[2] = 5*idx[2]+4;   vals3[2] = eM_0[r][2]/dt + user->L*user->kaeta*dt*eM_2_odd[r][2];
709:          */
710:         cols3[0] = 5*idx[0]+4;   vals3[0] = eM_0[r][0]/dt + user->L*user->kaeta*eM_2_odd[r][0];
711:         cols3[1] = 5*idx[1]+4;   vals3[1] = eM_0[r][1]/dt + user->L*user->kaeta*eM_2_odd[r][1];
712:         cols3[2] = 5*idx[2]+4;   vals3[2] = eM_0[r][2]/dt + user->L*user->kaeta*eM_2_odd[r][2];

714:         MatSetValuesLocal(M,1,&row,3,cols3,vals3,ADD_VALUES);


717:       } else {


720:         row     = 5*idx[r];
721:         cols[0] = 5*idx[0];     vals[0] = dt*eM_2_even[r][0]*cv_sum;
722:         cols[1] = 5*idx[1];     vals[1] = dt*eM_2_even[r][1]*cv_sum;
723:         cols[2] = 5*idx[2];     vals[2] = dt*eM_2_even[r][2]*cv_sum;
724:         cols[3] = 5*idx[0]+1;   vals[3] = eM_0[r][0];
725:         cols[4] = 5*idx[1]+1;   vals[4] = eM_0[r][1];
726:         cols[5] = 5*idx[2]+1;   vals[5] = eM_0[r][2];

728:         MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);

730:         row     = 5*idx[r]+1;
731:         cols[0] = 5*idx[0];     vals[0] = -1.0*eM_0[r][0];
732:         cols[1] = 5*idx[1];     vals[1] = -1.0*eM_0[r][1];
733:         cols[2] = 5*idx[2];     vals[2] = -1.0*eM_0[r][2];
734:         cols[3] = 5*idx[0]+1;   vals[3] =  user->kav*eM_2_even[r][0];
735:         cols[4] = 5*idx[1]+1;   vals[4] =  user->kav*eM_2_even[r][1];
736:         cols[5] = 5*idx[2]+1;   vals[5] =  user->kav*eM_2_even[r][2];

738:         MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);

740:         row     = 5*idx[r]+2;
741:         cols[0] = 5*idx[0]+2;   vals[0] = dt*eM_2_even[r][0]*ci_sum;
742:         cols[1] = 5*idx[1]+2;   vals[1] = dt*eM_2_even[r][1]*ci_sum;
743:         cols[2] = 5*idx[2]+2;   vals[2] = dt*eM_2_even[r][2]*ci_sum;
744:         cols[3] = 5*idx[0]+3;   vals[3] = eM_0[r][0];
745:         cols[4] = 5*idx[1]+3;   vals[4] = eM_0[r][1];
746:         cols[5] = 5*idx[2]+3;   vals[5] = eM_0[r][2];

748:         MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);

750:         row     = 5*idx[r]+3;
751:         cols[0] = 5*idx[0]+2;   vals[0] = -1.0*eM_0[r][0];
752:         cols[1] = 5*idx[1]+2;   vals[1] = -1.0*eM_0[r][1];
753:         cols[2] = 5*idx[2]+2;   vals[2] = -1.0*eM_0[r][2];
754:         cols[3] = 5*idx[0]+3;   vals[3] =  user->kai*eM_2_even[r][0];
755:         cols[4] = 5*idx[1]+3;   vals[4] =  user->kai*eM_2_even[r][1];
756:         cols[5] = 5*idx[2]+3;   vals[5] =  user->kai*eM_2_even[r][2];

758:         MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);

760:         row = 5*idx[r]+4;
761:         /*
762:         cols3[0] = 5*idx[0]+4;   vals3[0] = eM_0[r][0]/dt + user->L*user->kaeta*dt*eM_2_even[r][0];
763:         cols3[1] = 5*idx[1]+4;   vals3[1] = eM_0[r][1]/dt + user->L*user->kaeta*dt*eM_2_even[r][1];
764:         cols3[2] = 5*idx[2]+4;   vals3[2] = eM_0[r][2]/dt + user->L*user->kaeta*dt*eM_2_even[r][2];
765:          */
766:         cols3[0] = 5*idx[0]+4;   vals3[0] = eM_0[r][0]/dt + user->L*user->kaeta*eM_2_even[r][0];
767:         cols3[1] = 5*idx[1]+4;   vals3[1] = eM_0[r][1]/dt + user->L*user->kaeta*eM_2_even[r][1];
768:         cols3[2] = 5*idx[2]+4;   vals3[2] = eM_0[r][2]/dt + user->L*user->kaeta*eM_2_even[r][2];

770:         MatSetValuesLocal(M,1,&row,3,cols3,vals3,ADD_VALUES);

772:       }

774:     }
775:   }

777:   PetscFree(nodes);
778:   PetscFree(connect);

780:   VecRestoreArray(user->cv,&cv_p);
781:   VecRestoreArray(user->ci,&ci_p);
782:   MatAssemblyBegin(M_0,MAT_FINAL_ASSEMBLY);
783:   MatAssemblyEnd(M_0,MAT_FINAL_ASSEMBLY);

785:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
786:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);

788:   DMDARestoreElements(user->da1,&nele,&nen,&ele);
789:   return(0);
790: }


795: PetscErrorCode UpdateMatrices(AppCtx *user)
796: {
798:   PetscInt       i,j,n,Mda,Nda;

800:   PetscInt    idx[3],*nodes,*connect,k;
801:   PetscInt    ld,rd,lu,ru;
802:   PetscScalar eM_2_odd[3][3],eM_2_even[3][3],h,dt=user->dt;
803:   Mat         M=user->M;
804:   PetscScalar *cv_p,*ci_p,cv_sum,ci_sum;

807:   /* Create the mass matrix M_0 */
808:   MatGetLocalSize(M,&n,NULL);
809:   VecGetArray(user->cv,&cv_p);
810:   VecGetArray(user->ci,&ci_p);
811:   DMDAGetInfo(user->da1,NULL,&Mda,&Nda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);

813:   PetscMalloc1((Mda+1)*(Nda+1),&nodes);
814:   PetscMalloc1(Mda*Nda*2*3,&connect);

816:   h = 100.0/Mda;

818:   for (j=0; j < Nda; j++) {
819:     for (i=0; i < Mda; i++) nodes[j*(Mda+1)+i] = j*Mda+i;
820:     nodes[j*(Mda+1)+Mda] = j*Mda;
821:   }
822:   for (i=0; i < Mda; i++) nodes[Nda*(Mda+1)+i]=i;
823:   nodes[Nda*(Mda+1)+Mda]=0;


826:   k = 0;
827:   for (j=0; j<Nda; j++) {
828:     for (i=0; i<Mda; i++) {
829:       ld = nodes[j*(Mda+1)+i];
830:       rd = nodes[(j+1)*(Mda+1)+i];
831:       ru = nodes[(j+1)*(Mda+1)+i+1];
832:       lu = nodes[j*(Mda+1)+i+1];

834:       connect[k*6]   = ld;
835:       connect[k*6+1] = lu;
836:       connect[k*6+2] = rd;
837:       connect[k*6+3] = lu;
838:       connect[k*6+4] = ru;
839:       connect[k*6+5] = rd;

841:       k = k+1;
842:     }
843:   }

845:   for (k=0; k < Mda*Nda*2; k++) {
846:     idx[0] = connect[k*3];
847:     idx[1] = connect[k*3+1];
848:     idx[2] = connect[k*3+2];

850:     PetscInt    r,row,cols[3];
851:     PetscScalar vals[3];
852:     for (r=0; r<3; r++) {
853:       row     = 5*idx[r];
854:       cols[0] = 5*idx[0];     vals[0] = 0.0;
855:       cols[1] = 5*idx[1];     vals[1] = 0.0;
856:       cols[2] = 5*idx[2];     vals[2] = 0.0;

858:       /* Insert values in matrix M for 1st dof */
859:       MatSetValuesLocal(M,1,&row,3,cols,vals,INSERT_VALUES);

861:       row     = 5*idx[r]+2;
862:       cols[0] = 5*idx[0]+2;   vals[0] = 0.0;
863:       cols[1] = 5*idx[1]+2;   vals[1] = 0.0;
864:       cols[2] = 5*idx[2]+2;   vals[2] = 0.0;

866:       /* Insert values in matrix M for 3nd dof */
867:       MatSetValuesLocal(M,1,&row,3,cols,vals,INSERT_VALUES);
868:     }
869:   }

871:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
872:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);

874:   eM_2_odd[0][0] = 1.0;
875:   eM_2_odd[1][1] = eM_2_odd[2][2] = 0.5;
876:   eM_2_odd[0][1] = eM_2_odd[0][2] = eM_2_odd[1][0]= eM_2_odd[2][0] = -0.5;
877:   eM_2_odd[1][2] = eM_2_odd[2][1] = 0.0;

879:   eM_2_even[1][1] = 1.0;
880:   eM_2_even[0][0] = eM_2_even[2][2] = 0.5;
881:   eM_2_even[0][1] = eM_2_even[1][0] = eM_2_even[1][2] = eM_2_even[2][1] = -0.5;
882:   eM_2_even[0][2] = eM_2_even[2][0] = 0.0;


885:   /* Get local element info */
886:   for (k=0; k < Mda*Nda*2; k++) {
887:     idx[0] = connect[k*3];
888:     idx[1] = connect[k*3+1];
889:     idx[2] = connect[k*3+2];

891:     PetscInt    row,cols[3],r;
892:     PetscScalar vals[3];

894:     for (r=0; r<3; r++) {

896:       /* cv_sum = (1.0e-3+cv_p[idx[0]] + cv_p[idx[1]] + cv_p[idx[2]])*user->Dv/(3.0*user->kBT); */
897:       /* ci_sum = (1.0e-3+ci_p[idx[0]] + ci_p[idx[1]] + ci_p[idx[2]])*user->Di/(3.0*user->kBT); */
898:       cv_sum = .0000069*user->Dv/(user->kBT);
899:       ci_sum = .0000069*user->Di/user->kBT;

901:       if (k%2 == 0) { /* odd triangle */

903:         row     = 5*idx[r];
904:         cols[0] = 5*idx[0];     vals[0] = dt*eM_2_odd[r][0]*cv_sum;
905:         cols[1] = 5*idx[1];     vals[1] = dt*eM_2_odd[r][1]*cv_sum;
906:         cols[2] = 5*idx[2];     vals[2] = dt*eM_2_odd[r][2]*cv_sum;

908:         /* Insert values in matrix M for 1st dof */
909:         MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);

911:         row     = 5*idx[r]+2;
912:         cols[0] = 5*idx[0]+2;   vals[0] = dt*eM_2_odd[r][0]*ci_sum;
913:         cols[1] = 5*idx[1]+2;   vals[1] = dt*eM_2_odd[r][1]*ci_sum;
914:         cols[2] = 5*idx[2]+2;   vals[2] = dt*eM_2_odd[r][2]*ci_sum;

916:         MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);

918:       } else {
919:         row     = 5*idx[r];
920:         cols[0] = 5*idx[0];     vals[0] = dt*eM_2_even[r][0]*cv_sum;
921:         cols[1] = 5*idx[1];     vals[1] = dt*eM_2_even[r][1]*cv_sum;
922:         cols[2] = 5*idx[2];     vals[2] = dt*eM_2_even[r][2]*cv_sum;

924:         /* Insert values in matrix M for 1st dof */
925:         MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);

927:         row     = 5*idx[r]+2;
928:         cols[0] = 5*idx[0]+2;   vals[0] = dt*eM_2_even[r][0]*ci_sum;
929:         cols[1] = 5*idx[1]+2;   vals[1] = dt*eM_2_even[r][1]*ci_sum;
930:         cols[2] = 5*idx[2]+2;   vals[2] = dt*eM_2_even[r][2]*ci_sum;
931:         /* Insert values in matrix M for 3nd dof */
932:         MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);
933:       }
934:     }
935:   }

937:   PetscFree(nodes);
938:   PetscFree(connect);
939:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
940:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);
941:   VecRestoreArray(user->cv,&cv_p);
942:   VecRestoreArray(user->ci,&ci_p);
943:   return(0);
944: }