Actual source code: ex60.c
petsc-3.4.5 2014-06-29
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*,MatStructure*,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,DMDA_BOUNDARY_NONE,DMDA_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,DMDA_BOUNDARY_NONE,DMDA_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: DMCreateMatrix(user.da1,MATAIJ,&user.M);
124: /* Get the (usual) mass matrix structure from da2 */
125: DMCreateMatrix(user.da2,MATAIJ,&user.M_0);
126: SetInitialGuess(x,&user);
127: /* Form the jacobian matrix and M_0 */
128: SetUpMatrices(&user);
129: MatDuplicate(user.M,MAT_DO_NOT_COPY_VALUES,&J);
131: SNESCreate(PETSC_COMM_WORLD,&snes);
132: SNESSetDM(snes,user.da1);
134: SNESSetFunction(snes,r,FormFunction,(void*)&user);
135: SNESSetJacobian(snes,J,J,FormJacobian,(void*)&user);
137: SetVariableBounds(user.da1,xl,xu);
138: SNESVISetVariableBounds(snes,xl,xu);
139: SNESSetFromOptions(snes);
141: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_rand",FILE_MODE_WRITE,&view_rand);
142: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_mat",FILE_MODE_WRITE,&view_mat);
143: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_q",FILE_MODE_WRITE,&view_q);
144: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_out",FILE_MODE_WRITE,&view_out);
145: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_psi",FILE_MODE_WRITE,&view_psi);
147: while (t<user.T) {
148: SNESSetFunction(snes,r,FormFunction,(void*)&user);
149: SNESSetJacobian(snes,J,J,FormJacobian,(void*)&user);
151: SetRandomVectors(&user);
152: /* VecView(user.Pv,view_rand);
153: VecView(user.Pi,view_rand);
154: VecView(user.Piv,view_rand);*/
156: DPsi(&user);
157: /* VecView(user.DPsiv,view_psi);
158: VecView(user.DPsii,view_psi);
159: VecView(user.DPsieta,view_psi);*/
161: Update_q(&user);
162: /* VecView(user.q,view_q);
163: MatView(user.M,view_mat);*/
164: SNESSolve(snes,NULL,x);
165: SNESVIGetInactiveSet(snes,&inactiveconstraints);
166: ISGetSize(inactiveconstraints,&ninactiveconstraints);
167: /* if (ninactiveconstraints < .90*N) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP,"To many active constraints, model has become non-physical"); */
169: /* VecView(x,view_out);*/
170: VecView(x,PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD));
171: PetscInt its;
172: SNESGetIterationNumber(snes,&its);
173: PetscPrintf(PETSC_COMM_WORLD,"SNESVI solver converged at t = %5.4f in %d iterations\n",t,its);
175: Update_u(x,&user);
176: UpdateMatrices(&user);
177: t = t + user.dt;
178: }
180: PetscViewerDestroy(&view_rand);
181: PetscViewerDestroy(&view_mat);
182: PetscViewerDestroy(&view_q);
183: PetscViewerDestroy(&view_out);
184: PetscViewerDestroy(&view_psi);
186: VecDestroy(&x);
187: VecDestroy(&r);
188: VecDestroy(&xl);
189: VecDestroy(&xu);
190: VecDestroy(&user.q);
191: VecDestroy(&user.wv);
192: VecDestroy(&user.cv);
193: VecDestroy(&user.wi);
194: VecDestroy(&user.ci);
195: VecDestroy(&user.eta);
196: VecDestroy(&user.cvi);
197: VecDestroy(&user.DPsiv);
198: VecDestroy(&user.DPsii);
199: VecDestroy(&user.DPsieta);
200: VecDestroy(&user.Pv);
201: VecDestroy(&user.Pi);
202: VecDestroy(&user.Piv);
203: VecDestroy(&user.logcv);
204: VecDestroy(&user.logci);
205: VecDestroy(&user.logcvi);
206: VecDestroy(&user.work1);
207: VecDestroy(&user.work2);
208: VecDestroy(&user.Rr);
209: VecDestroy(&user.Riv);
210: MatDestroy(&user.M);
211: MatDestroy(&user.M_0);
212: DMDestroy(&user.da1);
213: DMDestroy(&user.da2);
215: PetscFinalize();
216: return 0;
217: }
221: PetscErrorCode Update_u(Vec X,AppCtx *user)
222: {
224: PetscInt i,n;
225: PetscScalar *xx,*wv_p,*cv_p,*wi_p,*ci_p,*eta_p;
228: VecGetLocalSize(user->wv,&n);
229: VecGetArray(X,&xx);
230: VecGetArray(user->wv,&wv_p);
231: VecGetArray(user->cv,&cv_p);
232: VecGetArray(user->wi,&wi_p);
233: VecGetArray(user->ci,&ci_p);
234: VecGetArray(user->eta,&eta_p);
237: for (i=0; i<n; i++) {
238: wv_p[i] = xx[5*i];
239: cv_p[i] = xx[5*i+1];
240: wi_p[i] = xx[5*i+2];
241: ci_p[i] = xx[5*i+3];
242: eta_p[i] = xx[5*i+4];
243: }
244: VecRestoreArray(X,&xx);
245: VecRestoreArray(user->wv,&wv_p);
246: VecRestoreArray(user->cv,&cv_p);
247: VecRestoreArray(user->wi,&wi_p);
248: VecRestoreArray(user->ci,&ci_p);
249: VecRestoreArray(user->eta,&eta_p);
250: return(0);
251: }
255: PetscErrorCode Update_q(AppCtx *user)
256: {
258: PetscScalar *q_p,*w1,*w2;
259: PetscInt i,n;
262: VecPointwiseMult(user->Rr,user->eta,user->eta);
263: VecScale(user->Rr,user->Rsurf);
264: VecShift(user->Rr,user->Rbulk);
265: VecPointwiseMult(user->Riv,user->cv,user->ci);
266: VecPointwiseMult(user->Riv,user->Rr,user->Riv);
268: VecGetArray(user->q,&q_p);
269: VecGetArray(user->work1,&w1);
270: VecGetArray(user->work2,&w2);
272: VecCopy(user->cv,user->work1);
273: VecAXPY(user->work1,1.0,user->Pv);
274: VecScale(user->work1,-1.0);
275: MatMult(user->M_0,user->work1,user->work2);
276: VecGetLocalSize(user->work1,&n);
278: for (i=0; i<n; i++) q_p[5*i]=w2[i];
280: MatMult(user->M_0,user->DPsiv,user->work1);
281: for (i=0; i<n; i++) q_p[5*i+1]=w1[i];
283: VecCopy(user->ci,user->work1);
284: VecAXPY(user->work1,1.0,user->Pi);
285: VecScale(user->work1,-1.0);
286: MatMult(user->M_0,user->work1,user->work2);
287: for (i=0; i<n; i++) q_p[5*i+2]=w2[i];
289: MatMult(user->M_0,user->DPsii,user->work1);
290: for (i=0; i<n; i++) q_p[5*i+3]=w1[i];
292: VecCopy(user->eta,user->work1);
293: VecScale(user->work1,-1.0/user->dt);
294: VecAXPY(user->work1,user->L,user->DPsieta);
295: VecAXPY(user->work1,-1.0,user->Piv);
296: MatMult(user->M_0,user->work1,user->work2);
297: for (i=0; i<n; i++) q_p[5*i+4]=w2[i];
299: VecRestoreArray(user->q,&q_p);
300: VecRestoreArray(user->work1,&w1);
301: VecRestoreArray(user->work2,&w2);
302: return(0);
303: }
307: PetscErrorCode DPsi(AppCtx *user)
308: {
310: PetscScalar Evf=user->Evf,Eif=user->Eif,kBT=user->kBT,A=user->A;
311: PetscScalar *cv_p,*ci_p,*eta_p,*logcv_p,*logci_p,*logcvi_p,*DPsiv_p,*DPsii_p,*DPsieta_p;
312: PetscInt n,i;
315: VecGetLocalSize(user->cv,&n);
316: VecGetArray(user->cv,&cv_p);
317: VecGetArray(user->ci,&ci_p);
318: VecGetArray(user->eta,&eta_p);
319: VecGetArray(user->logcv,&logcv_p);
320: VecGetArray(user->logci,&logci_p);
321: VecGetArray(user->logcvi,&logcvi_p);
322: VecGetArray(user->DPsiv,&DPsiv_p);
323: VecGetArray(user->DPsii,&DPsii_p);
324: VecGetArray(user->DPsieta,&DPsieta_p);
326: Llog(user->cv,user->logcv);
328: Llog(user->ci,user->logci);
331: VecCopy(user->cv,user->cvi);
332: VecAXPY(user->cvi,1.0,user->ci);
333: VecScale(user->cvi,-1.0);
334: VecShift(user->cvi,1.0);
335: Llog(user->cvi,user->logcvi);
337: for (i=0; i<n; i++)
338: {
339: 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);
340: 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];
342: 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]);
343: }
345: VecRestoreArray(user->cv,&cv_p);
346: VecRestoreArray(user->ci,&ci_p);
347: VecRestoreArray(user->eta,&eta_p);
348: VecRestoreArray(user->logcv,&logcv_p);
349: VecRestoreArray(user->logci,&logci_p);
350: VecRestoreArray(user->logcvi,&logcvi_p);
351: VecRestoreArray(user->DPsiv,&DPsiv_p);
352: VecRestoreArray(user->DPsii,&DPsii_p);
353: VecRestoreArray(user->DPsieta,&DPsieta_p);
354: return(0);
355: }
360: PetscErrorCode Llog(Vec X, Vec Y)
361: {
363: PetscScalar *x,*y;
364: PetscInt n,i;
367: VecGetArray(X,&x);
368: VecGetArray(Y,&y);
369: VecGetLocalSize(X,&n);
370: for (i=0; i<n; i++) {
371: if (x[i] < 1.0e-12) y[i] = log(1.0e-12);
372: else y[i] = log(x[i]);
373: }
374: return(0);
375: }
380: PetscErrorCode SetInitialGuess(Vec X,AppCtx *user)
381: {
383: PetscInt n,i;
384: PetscScalar *xx,*cv_p,*ci_p,*wv_p,*wi_p;
385: PetscViewer view;
386: PetscScalar initv = .00069;
389: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"file_initial",FILE_MODE_WRITE,&view);
390: VecGetLocalSize(X,&n);
392: VecSet(user->cv,initv);
393: VecSet(user->ci,initv);
394: VecSet(user->eta,0.0);
396: DPsi(user);
397: VecCopy(user->DPsiv,user->wv);
398: VecCopy(user->DPsii,user->wi);
400: VecGetArray(X,&xx);
401: VecGetArray(user->cv,&cv_p);
402: VecGetArray(user->ci,&ci_p);
403: VecGetArray(user->wv,&wv_p);
404: VecGetArray(user->wi,&wi_p);
405: for (i=0; i<n/5; i++) {
406: xx[5*i] =wv_p[i];
407: xx[5*i+1]=cv_p[i];
408: xx[5*i+2]=wi_p[i];
409: xx[5*i+3]=ci_p[i];
410: xx[5*i+4]=0.0;
411: }
413: VecView(user->wv,view);
414: VecView(user->cv,view);
415: VecView(user->wi,view);
416: VecView(user->ci,view);
417: PetscViewerDestroy(&view);
419: VecRestoreArray(X,&xx);
420: VecRestoreArray(user->cv,&cv_p);
421: VecRestoreArray(user->ci,&ci_p);
422: VecRestoreArray(user->wv,&wv_p);
423: VecRestoreArray(user->wi,&wi_p);
424: return(0);
425: }
429: PetscErrorCode SetRandomVectors(AppCtx *user)
430: {
432: PetscInt i,n,count=0;
433: PetscScalar *w1,*w2,*Pv_p,*eta_p;
436: VecSetRandom(user->work1,NULL);
437: VecSetRandom(user->work2,NULL);
438: VecGetArray(user->work1,&w1);
439: VecGetArray(user->work2,&w2);
440: VecGetArray(user->Pv,&Pv_p);
441: VecGetArray(user->eta,&eta_p);
442: VecGetLocalSize(user->work1,&n);
443: for (i=0; i<n; i++) {
445: if (eta_p[i]>=0.8 || w1[i]>user->P_casc) Pv_p[i]=0;
446: else {
447: Pv_p[i]=w2[i]*user->VG;
448: count =count+1;
449: }
451: }
453: VecCopy(user->Pv,user->Pi);
454: VecScale(user->Pi,0.9);
455: VecPointwiseMult(user->Piv,user->Pi,user->Pv);
456: VecRestoreArray(user->work1,&w1);
457: VecRestoreArray(user->work2,&w2);
458: VecRestoreArray(user->Pv,&Pv_p);
459: VecRestoreArray(user->eta,&eta_p);
460: return(0);
462: }
466: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ctx)
467: {
469: AppCtx *user=(AppCtx*)ctx;
472: MatMultAdd(user->M,X,user->q,F);
473: return(0);
474: }
478: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat *J,Mat *B,MatStructure *flg,void *ctx)
479: {
481: AppCtx *user=(AppCtx*)ctx;
484: *flg = SAME_NONZERO_PATTERN;
485: MatCopy(user->M,*J,*flg);
486: MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
487: MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
488: return(0);
489: }
492: PetscErrorCode SetVariableBounds(DM da,Vec xl,Vec xu)
493: {
495: PetscScalar ***l,***u;
496: PetscInt xs,xm,ys,ym;
497: PetscInt j,i;
500: DMDAVecGetArrayDOF(da,xl,&l);
501: DMDAVecGetArrayDOF(da,xu,&u);
503: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
505: for (j=ys; j<ys+ym; j++) {
506: for (i=xs; i < xs+xm; i++) {
507: l[j][i][0] = -SNES_VI_INF;
508: l[j][i][1] = 0.0;
509: l[j][i][2] = -SNES_VI_INF;
510: l[j][i][3] = 0.0;
511: l[j][i][4] = 0.0;
512: u[j][i][0] = SNES_VI_INF;
513: u[j][i][1] = 1.0;
514: u[j][i][2] = SNES_VI_INF;
515: u[j][i][3] = 1.0;
516: u[j][i][4] = 1.0;
517: }
518: }
521: DMDAVecRestoreArrayDOF(da,xl,&l);
522: DMDAVecRestoreArrayDOF(da,xu,&u);
523: return(0);
524: }
528: PetscErrorCode GetParams(AppCtx *user)
529: {
531: PetscBool flg;
534: /* Set default parameters */
535: user->xmin = 0.0; user->xmax = 1.0;
536: user->ymin = 0.0; user->ymax = 1.0;
537: user->Dv = 1.0; user->Di=4.0;
538: user->Evf = 0.8; user->Eif = 1.2;
539: user->A = 1.0;
540: user->kBT = 0.11;
541: user->kav = 1.0; user->kai = 1.0; user->kaeta = 1.0;
542: user->Rsurf = 10.0; user->Rbulk = 1.0;
543: user->L = 10.0; user->P_casc = 0.05;
544: user->T = 1.0e-2; user->dt = 1.0e-4;
545: user->VG = 100.0;
547: PetscOptionsGetReal(NULL,"-xmin",&user->xmin,&flg);
548: PetscOptionsGetReal(NULL,"-xmax",&user->xmax,&flg);
549: PetscOptionsGetReal(NULL,"-T",&user->T,&flg);
550: PetscOptionsGetReal(NULL,"-dt",&user->dt,&flg);
551: PetscOptionsGetReal(NULL,"-P_casc",&user->P_casc,&flg);
552: PetscOptionsGetReal(NULL,"-VG",&user->VG,&flg);
553: return(0);
554: }
559: PetscErrorCode SetUpMatrices(AppCtx *user)
560: {
562: PetscInt nele,nen,i,j,n;
563: const PetscInt *ele;
564: PetscScalar dt=user->dt,hx,hy;
566: PetscInt idx[3],*nodes, *connect, k;
567: PetscScalar eM_0[3][3],eM_2_even[3][3],eM_2_odd[3][3];
568: PetscScalar cv_sum, ci_sum;
569: Mat M =user->M;
570: Mat M_0=user->M_0;
571: PetscInt Mda=user->Mda, Nda=user->Nda, ld, rd, ru, lu;
572: PetscScalar *cv_p,*ci_p;
575: /* MatSetOption(M,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
576: MatSetOption(M_0,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);*/
578: /* Create the mass matrix M_0 */
579: VecGetArray(user->cv,&cv_p);
580: VecGetArray(user->ci,&ci_p);
581: MatGetLocalSize(M,&n,NULL);
582: DMDAGetInfo(user->da1,NULL,&Mda,&Nda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
584: PetscMalloc((Mda+1)*(Nda+1)*sizeof(PetscInt),&nodes);
585: PetscMalloc(Mda*Nda*2*3*sizeof(PetscInt),&connect);
586: hx = (user->xmax-user->xmin)/Mda;
587: hy = (user->ymax-user->ymin)/Nda;
588: for (j=0; j < Nda; j++) {
589: for (i=0; i < Mda; i++) nodes[j*(Mda+1)+i] = j*Mda+i;
590: nodes[j*(Mda+1)+Mda] = j*Mda;
591: }
593: for (i=0; i < Mda; i++) nodes[Nda*(Mda+1)+i] = i;
595: nodes[Nda*(Mda+1)+Mda] = 0;
597: k = 0;
598: for (j=0; j<Nda; j++) {
599: for (i=0; i<Mda; i++) {
601: /* ld = nodes[j][i]; */
602: ld = nodes[j*(Mda+1)+i];
603: /* rd = nodes[j+1][i]; */
604: rd = nodes[(j+1)*(Mda+1)+i];
605: /* ru = nodes[j+1][i+1]; */
606: ru = nodes[(j+1)*(Mda+1)+i+1];
607: /* lu = nodes[j][i+1]; */
608: lu = nodes[j*(Mda+1)+i+1];
610: /* connect[k][0]=ld; */
611: connect[k*6]=ld;
612: /* connect[k][1]=lu; */
613: connect[k*6+1]=lu;
614: /* connect[k][2]=ru; */
615: connect[k*6+2]=rd;
616: connect[k*6+3]=lu;
617: connect[k*6+4]=ru;
618: connect[k*6+5]=rd;
620: k = k+1;
621: }
622: }
625: eM_0[0][0]=eM_0[1][1]=eM_0[2][2]=hx*hy/12.0;
626: 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;
628: eM_2_odd[0][0] = 1.0;
629: eM_2_odd[1][1] = eM_2_odd[2][2] = 0.5;
630: eM_2_odd[0][1] = eM_2_odd[0][2] = eM_2_odd[1][0]= eM_2_odd[2][0] = -0.5;
631: eM_2_odd[1][2] = eM_2_odd[2][1] = 0.0;
633: eM_2_even[1][1] = 1.0;
634: eM_2_even[0][0] = eM_2_even[2][2] = 0.5;
635: eM_2_even[0][1] = eM_2_even[1][0] = eM_2_even[1][2] = eM_2_even[2][1] = -0.5;
636: eM_2_even[0][2] = eM_2_even[2][0] = 0.0;
639: for (k=0; k < Mda*Nda*2; k++) {
640: idx[0] = connect[k*3];
641: idx[1] = connect[k*3+1];
642: idx[2] = connect[k*3+2];
644: PetscInt row,cols[6],r,row_M_0,cols3[3];
645: PetscScalar vals[6],vals_M_0[3],vals3[3];
647: for (r=0; r<3; r++) {
648: row_M_0 = connect[k*3+r];
650: vals_M_0[0]=eM_0[r][0];
651: vals_M_0[1]=eM_0[r][1];
652: vals_M_0[2]=eM_0[r][2];
655: MatSetValues(M_0,1,&row_M_0,3,idx,vals_M_0,ADD_VALUES);
657: /* cv_sum = (cv_p[idx[0]] + cv_p[idx[1]] + cv_p[idx[2]])*user->Dv/(3.0*user->kBT); */
658: /* ci_sum = (ci_p[idx[0]] + ci_p[idx[1]] + ci_p[idx[2]])*user->Di/(3.0*user->kBT); */
659: cv_sum = .0000069*user->Dv/user->kBT;
660: ci_sum = .0000069*user->Di/user->kBT;
662: if (k%2 == 0) {
663: row = 5*idx[r];
664: cols[0] = 5*idx[0]; vals[0] = dt*eM_2_odd[r][0]*cv_sum;
665: cols[1] = 5*idx[1]; vals[1] = dt*eM_2_odd[r][1]*cv_sum;
666: cols[2] = 5*idx[2]; vals[2] = dt*eM_2_odd[r][2]*cv_sum;
667: cols[3] = 5*idx[0]+1; vals[3] = eM_0[r][0];
668: cols[4] = 5*idx[1]+1; vals[4] = eM_0[r][1];
669: cols[5] = 5*idx[2]+1; vals[5] = eM_0[r][2];
671: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
673: row = 5*idx[r]+1;
674: cols[0] = 5*idx[0]; vals[0] = -1.0*eM_0[r][0];
675: cols[1] = 5*idx[1]; vals[1] = -1.0*eM_0[r][1];
676: cols[2] = 5*idx[2]; vals[2] = -1.0*eM_0[r][2];
677: cols[3] = 5*idx[0]+1; vals[3] = user->kav*eM_2_odd[r][0];
678: cols[4] = 5*idx[1]+1; vals[4] = user->kav*eM_2_odd[r][1];
679: cols[5] = 5*idx[2]+1; vals[5] = user->kav*eM_2_odd[r][2];
681: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
683: row = 5*idx[r]+2;
684: cols[0] = 5*idx[0]+2; vals[0] = dt*eM_2_odd[r][0]*ci_sum;
685: cols[1] = 5*idx[1]+2; vals[1] = dt*eM_2_odd[r][1]*ci_sum;
686: cols[2] = 5*idx[2]+2; vals[2] = dt*eM_2_odd[r][2]*ci_sum;
687: cols[3] = 5*idx[0]+3; vals[3] = eM_0[r][0];
688: cols[4] = 5*idx[1]+3; vals[4] = eM_0[r][1];
689: cols[5] = 5*idx[2]+3; vals[5] = eM_0[r][2];
691: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
693: row = 5*idx[r]+3;
694: cols[0] = 5*idx[0]+2; vals[0] = -1.0*eM_0[r][0];
695: cols[1] = 5*idx[1]+2; vals[1] = -1.0*eM_0[r][1];
696: cols[2] = 5*idx[2]+2; vals[2] = -1.0*eM_0[r][2];
697: cols[3] = 5*idx[0]+3; vals[3] = user->kai*eM_2_odd[r][0];
698: cols[4] = 5*idx[1]+3; vals[4] = user->kai*eM_2_odd[r][1];
699: cols[5] = 5*idx[2]+3; vals[5] = user->kai*eM_2_odd[r][2];
701: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
703: row = 5*idx[r]+4;
704: /*
705: cols3[0] = 5*idx[0]+4; vals3[0] = eM_0[r][0]/dt + user->L*user->kaeta*dt*eM_2_odd[r][0];
706: cols3[1] = 5*idx[1]+4; vals3[1] = eM_0[r][1]/dt + user->L*user->kaeta*dt*eM_2_odd[r][1];
707: cols3[2] = 5*idx[2]+4; vals3[2] = eM_0[r][2]/dt + user->L*user->kaeta*dt*eM_2_odd[r][2];
708: */
709: cols3[0] = 5*idx[0]+4; vals3[0] = eM_0[r][0]/dt + user->L*user->kaeta*eM_2_odd[r][0];
710: cols3[1] = 5*idx[1]+4; vals3[1] = eM_0[r][1]/dt + user->L*user->kaeta*eM_2_odd[r][1];
711: cols3[2] = 5*idx[2]+4; vals3[2] = eM_0[r][2]/dt + user->L*user->kaeta*eM_2_odd[r][2];
713: MatSetValuesLocal(M,1,&row,3,cols3,vals3,ADD_VALUES);
716: } else {
719: row = 5*idx[r];
720: cols[0] = 5*idx[0]; vals[0] = dt*eM_2_even[r][0]*cv_sum;
721: cols[1] = 5*idx[1]; vals[1] = dt*eM_2_even[r][1]*cv_sum;
722: cols[2] = 5*idx[2]; vals[2] = dt*eM_2_even[r][2]*cv_sum;
723: cols[3] = 5*idx[0]+1; vals[3] = eM_0[r][0];
724: cols[4] = 5*idx[1]+1; vals[4] = eM_0[r][1];
725: cols[5] = 5*idx[2]+1; vals[5] = eM_0[r][2];
727: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
729: row = 5*idx[r]+1;
730: cols[0] = 5*idx[0]; vals[0] = -1.0*eM_0[r][0];
731: cols[1] = 5*idx[1]; vals[1] = -1.0*eM_0[r][1];
732: cols[2] = 5*idx[2]; vals[2] = -1.0*eM_0[r][2];
733: cols[3] = 5*idx[0]+1; vals[3] = user->kav*eM_2_even[r][0];
734: cols[4] = 5*idx[1]+1; vals[4] = user->kav*eM_2_even[r][1];
735: cols[5] = 5*idx[2]+1; vals[5] = user->kav*eM_2_even[r][2];
737: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
739: row = 5*idx[r]+2;
740: cols[0] = 5*idx[0]+2; vals[0] = dt*eM_2_even[r][0]*ci_sum;
741: cols[1] = 5*idx[1]+2; vals[1] = dt*eM_2_even[r][1]*ci_sum;
742: cols[2] = 5*idx[2]+2; vals[2] = dt*eM_2_even[r][2]*ci_sum;
743: cols[3] = 5*idx[0]+3; vals[3] = eM_0[r][0];
744: cols[4] = 5*idx[1]+3; vals[4] = eM_0[r][1];
745: cols[5] = 5*idx[2]+3; vals[5] = eM_0[r][2];
747: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
749: row = 5*idx[r]+3;
750: cols[0] = 5*idx[0]+2; vals[0] = -1.0*eM_0[r][0];
751: cols[1] = 5*idx[1]+2; vals[1] = -1.0*eM_0[r][1];
752: cols[2] = 5*idx[2]+2; vals[2] = -1.0*eM_0[r][2];
753: cols[3] = 5*idx[0]+3; vals[3] = user->kai*eM_2_even[r][0];
754: cols[4] = 5*idx[1]+3; vals[4] = user->kai*eM_2_even[r][1];
755: cols[5] = 5*idx[2]+3; vals[5] = user->kai*eM_2_even[r][2];
757: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
759: row = 5*idx[r]+4;
760: /*
761: cols3[0] = 5*idx[0]+4; vals3[0] = eM_0[r][0]/dt + user->L*user->kaeta*dt*eM_2_even[r][0];
762: cols3[1] = 5*idx[1]+4; vals3[1] = eM_0[r][1]/dt + user->L*user->kaeta*dt*eM_2_even[r][1];
763: cols3[2] = 5*idx[2]+4; vals3[2] = eM_0[r][2]/dt + user->L*user->kaeta*dt*eM_2_even[r][2];
764: */
765: cols3[0] = 5*idx[0]+4; vals3[0] = eM_0[r][0]/dt + user->L*user->kaeta*eM_2_even[r][0];
766: cols3[1] = 5*idx[1]+4; vals3[1] = eM_0[r][1]/dt + user->L*user->kaeta*eM_2_even[r][1];
767: cols3[2] = 5*idx[2]+4; vals3[2] = eM_0[r][2]/dt + user->L*user->kaeta*eM_2_even[r][2];
769: MatSetValuesLocal(M,1,&row,3,cols3,vals3,ADD_VALUES);
771: }
773: }
774: }
776: PetscFree(nodes);
777: PetscFree(connect);
779: VecRestoreArray(user->cv,&cv_p);
780: VecRestoreArray(user->ci,&ci_p);
781: MatAssemblyBegin(M_0,MAT_FINAL_ASSEMBLY);
782: MatAssemblyEnd(M_0,MAT_FINAL_ASSEMBLY);
784: MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
785: MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);
787: DMDARestoreElements(user->da1,&nele,&nen,&ele);
788: return(0);
789: }
794: PetscErrorCode UpdateMatrices(AppCtx *user)
795: {
797: PetscInt i,j,n,Mda,Nda;
799: PetscInt idx[3],*nodes,*connect,k;
800: PetscInt ld,rd,lu,ru;
801: PetscScalar eM_2_odd[3][3],eM_2_even[3][3],h,dt=user->dt;
802: Mat M=user->M;
803: PetscScalar *cv_p,*ci_p,cv_sum,ci_sum;
806: /* Create the mass matrix M_0 */
807: MatGetLocalSize(M,&n,NULL);
808: VecGetArray(user->cv,&cv_p);
809: VecGetArray(user->ci,&ci_p);
810: DMDAGetInfo(user->da1,NULL,&Mda,&Nda,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
812: PetscMalloc((Mda+1)*(Nda+1)*sizeof(PetscInt),&nodes);
813: PetscMalloc(Mda*Nda*2*3*sizeof(PetscInt),&connect);
815: h = 100.0/Mda;
817: for (j=0; j < Nda; j++) {
818: for (i=0; i < Mda; i++) nodes[j*(Mda+1)+i] = j*Mda+i;
819: nodes[j*(Mda+1)+Mda] = j*Mda;
820: }
821: for (i=0; i < Mda; i++) nodes[Nda*(Mda+1)+i]=i;
822: nodes[Nda*(Mda+1)+Mda]=0;
825: k = 0;
826: for (j=0; j<Nda; j++) {
827: for (i=0; i<Mda; i++) {
828: ld = nodes[j*(Mda+1)+i];
829: rd = nodes[(j+1)*(Mda+1)+i];
830: ru = nodes[(j+1)*(Mda+1)+i+1];
831: lu = nodes[j*(Mda+1)+i+1];
833: connect[k*6] = ld;
834: connect[k*6+1] = lu;
835: connect[k*6+2] = rd;
836: connect[k*6+3] = lu;
837: connect[k*6+4] = ru;
838: connect[k*6+5] = rd;
840: k = k+1;
841: }
842: }
844: for (k=0; k < Mda*Nda*2; k++) {
845: idx[0] = connect[k*3];
846: idx[1] = connect[k*3+1];
847: idx[2] = connect[k*3+2];
849: PetscInt r,row,cols[3];
850: PetscScalar vals[3];
851: for (r=0; r<3; r++) {
852: row = 5*idx[r];
853: cols[0] = 5*idx[0]; vals[0] = 0.0;
854: cols[1] = 5*idx[1]; vals[1] = 0.0;
855: cols[2] = 5*idx[2]; vals[2] = 0.0;
857: /* Insert values in matrix M for 1st dof */
858: MatSetValuesLocal(M,1,&row,3,cols,vals,INSERT_VALUES);
860: row = 5*idx[r]+2;
861: cols[0] = 5*idx[0]+2; vals[0] = 0.0;
862: cols[1] = 5*idx[1]+2; vals[1] = 0.0;
863: cols[2] = 5*idx[2]+2; vals[2] = 0.0;
865: /* Insert values in matrix M for 3nd dof */
866: MatSetValuesLocal(M,1,&row,3,cols,vals,INSERT_VALUES);
867: }
868: }
870: MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
871: MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);
873: eM_2_odd[0][0] = 1.0;
874: eM_2_odd[1][1] = eM_2_odd[2][2] = 0.5;
875: eM_2_odd[0][1] = eM_2_odd[0][2] = eM_2_odd[1][0]= eM_2_odd[2][0] = -0.5;
876: eM_2_odd[1][2] = eM_2_odd[2][1] = 0.0;
878: eM_2_even[1][1] = 1.0;
879: eM_2_even[0][0] = eM_2_even[2][2] = 0.5;
880: eM_2_even[0][1] = eM_2_even[1][0] = eM_2_even[1][2] = eM_2_even[2][1] = -0.5;
881: eM_2_even[0][2] = eM_2_even[2][0] = 0.0;
884: /* Get local element info */
885: for (k=0; k < Mda*Nda*2; k++) {
886: idx[0] = connect[k*3];
887: idx[1] = connect[k*3+1];
888: idx[2] = connect[k*3+2];
890: PetscInt row,cols[3],r;
891: PetscScalar vals[3];
893: for (r=0; r<3; r++) {
895: /* cv_sum = (1.0e-3+cv_p[idx[0]] + cv_p[idx[1]] + cv_p[idx[2]])*user->Dv/(3.0*user->kBT); */
896: /* ci_sum = (1.0e-3+ci_p[idx[0]] + ci_p[idx[1]] + ci_p[idx[2]])*user->Di/(3.0*user->kBT); */
897: cv_sum = .0000069*user->Dv/(user->kBT);
898: ci_sum = .0000069*user->Di/user->kBT;
900: if (k%2 == 0) { /* odd triangle */
902: row = 5*idx[r];
903: cols[0] = 5*idx[0]; vals[0] = dt*eM_2_odd[r][0]*cv_sum;
904: cols[1] = 5*idx[1]; vals[1] = dt*eM_2_odd[r][1]*cv_sum;
905: cols[2] = 5*idx[2]; vals[2] = dt*eM_2_odd[r][2]*cv_sum;
907: /* Insert values in matrix M for 1st dof */
908: MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);
910: row = 5*idx[r]+2;
911: cols[0] = 5*idx[0]+2; vals[0] = dt*eM_2_odd[r][0]*ci_sum;
912: cols[1] = 5*idx[1]+2; vals[1] = dt*eM_2_odd[r][1]*ci_sum;
913: cols[2] = 5*idx[2]+2; vals[2] = dt*eM_2_odd[r][2]*ci_sum;
915: MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);
917: } else {
918: row = 5*idx[r];
919: cols[0] = 5*idx[0]; vals[0] = dt*eM_2_even[r][0]*cv_sum;
920: cols[1] = 5*idx[1]; vals[1] = dt*eM_2_even[r][1]*cv_sum;
921: cols[2] = 5*idx[2]; vals[2] = dt*eM_2_even[r][2]*cv_sum;
923: /* Insert values in matrix M for 1st dof */
924: MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);
926: row = 5*idx[r]+2;
927: cols[0] = 5*idx[0]+2; vals[0] = dt*eM_2_even[r][0]*ci_sum;
928: cols[1] = 5*idx[1]+2; vals[1] = dt*eM_2_even[r][1]*ci_sum;
929: cols[2] = 5*idx[2]+2; vals[2] = dt*eM_2_even[r][2]*ci_sum;
930: /* Insert values in matrix M for 3nd dof */
931: MatSetValuesLocal(M,1,&row,3,cols,vals,ADD_VALUES);
932: }
933: }
934: }
936: PetscFree(nodes);
937: PetscFree(connect);
938: MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
939: MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);
940: VecRestoreArray(user->cv,&cv_p);
941: VecRestoreArray(user->ci,&ci_p);
942: return(0);
943: }