Actual source code: ex63.c
petsc-3.4.5 2014-06-29
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: }