Actual source code: ex54.c
petsc-3.5.4 2015-05-23
1: static char help[] = "Cahn-Hilliard-2d problem 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: Run with for example: -pc_type mg -pc_mg_galerkin -T .01 -da_grid_x 65 -da_grid_y 65 -pc_mg_levels 4 -ksp_type fgmres -snes_atol 1.e-14 -mat_no_inode
13: */
15: #include <petscsnes.h>
16: #include <petscdmda.h>
18: typedef struct {
19: PetscReal dt,T; /* Time step and end time */
20: DM da;
21: Mat M; /* Jacobian matrix */
22: Mat M_0;
23: Vec q,u,work1;
24: PetscScalar gamma,theta_c; /* physics parameters */
25: PetscReal xmin,xmax,ymin,ymax;
26: PetscBool tsmonitor;
27: } AppCtx;
29: PetscErrorCode GetParams(AppCtx*);
30: PetscErrorCode SetVariableBounds(DM,Vec,Vec);
31: PetscErrorCode SetUpMatrices(AppCtx*);
32: PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
33: PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);
34: PetscErrorCode SetInitialGuess(Vec,AppCtx*);
35: PetscErrorCode Update_q(Vec,Vec,Mat,AppCtx*);
36: PetscLogEvent event_update_q;
40: int main(int argc, char **argv)
41: {
42: PetscErrorCode ierr;
43: Vec x,r; /* Solution and residual vectors */
44: SNES snes; /* Nonlinear solver context */
45: AppCtx user; /* Application context */
46: Vec xl,xu; /* Upper and lower bounds on variables */
47: Mat J;
48: PetscReal t=0.0;
49: PETSC_UNUSED PetscLogStage stage_timestep;
50: PetscInt its;
52: PetscInitialize(&argc,&argv, (char*)0, help);
54: /* Get physics and time parameters */
55: GetParams(&user);
56: /* Create a 2D DA with dof = 2 */
57: DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,-4,-4,PETSC_DECIDE,PETSC_DECIDE,2,1,NULL,NULL,&user.da);
58: /* Set Element type (triangular) */
59: DMDASetElementType(user.da,DMDA_ELEMENT_P1);
61: /* Set x and y coordinates */
62: DMDASetUniformCoordinates(user.da,user.xmin,user.xmax,user.ymin,user.ymax,0.0,1.0);
64: /* Get global vector x from DM and duplicate vectors r,xl,xu */
65: DMCreateGlobalVector(user.da,&x);
66: VecDuplicate(x,&r);
67: VecDuplicate(x,&xl);
68: VecDuplicate(x,&xu);
69: VecDuplicate(x,&user.q);
71: /* Get Jacobian matrix structure from the da */
72: DMSetMatType(user.da,MATAIJ);
73: DMCreateMatrix(user.da,&user.M);
74: /* Form the jacobian matrix and M_0 */
75: SetUpMatrices(&user);
76: MatDuplicate(user.M,MAT_DO_NOT_COPY_VALUES,&J);
78: /* Create nonlinear solver context */
79: SNESCreate(PETSC_COMM_WORLD,&snes);
80: SNESSetDM(snes,user.da);
82: /* Set Function evaluation and jacobian evaluation routines */
83: SNESSetFunction(snes,r,FormFunction,(void*)&user);
84: SNESSetJacobian(snes,J,J,FormJacobian,(void*)&user);
86: /* Set the boundary conditions */
87: SetVariableBounds(user.da,xl,xu);
88: SNESVISetVariableBounds(snes,xl,xu);
89: SNESSetFromOptions(snes);
91: SetInitialGuess(x,&user);
92: PetscLogStageRegister("Time stepping",&stage_timestep);
93: PetscLogEventRegister("Update q",MAT_CLASSID,&event_update_q);
94: PetscLogStagePush(stage_timestep);
95: /* Begin time loop */
96: while (t < user.T) {
97: Update_q(user.q,user.u,user.M_0,&user);
98: SNESSolve(snes,NULL,x);
99: SNESGetIterationNumber(snes,&its);
100: if (user.tsmonitor) {
101: PetscPrintf(PETSC_COMM_WORLD,"SNESVI solver converged at t = %5.4f in %d iterations\n",t,its);
102: }
103: VecStrideGather(x,1,user.u,INSERT_VALUES);
104: t = t + user.dt;
105: }
106: PetscLogStagePop();
108: VecDestroy(&x);
109: VecDestroy(&r);
110: VecDestroy(&xl);
111: VecDestroy(&xu);
112: VecDestroy(&user.q);
113: VecDestroy(&user.u);
114: VecDestroy(&user.work1);
115: MatDestroy(&user.M);
116: MatDestroy(&user.M_0);
117: MatDestroy(&J);
118: DMDestroy(&user.da);
119: SNESDestroy(&snes);
120: PetscFinalize();
121: return 0;
122: }
126: PetscErrorCode Update_q(Vec q,Vec u,Mat M_0,AppCtx *user)
127: {
129: PetscScalar *q_arr,*w_arr;
130: PetscInt i,n;
133: PetscLogEventBegin(event_update_q,0,0,0,0);
134: MatMult(M_0,u,user->work1);
135: VecScale(user->work1,-1.0);
136: VecGetLocalSize(u,&n);
137: VecGetArray(q,&q_arr);
138: VecGetArray(user->work1,&w_arr);
139: for (i=0; i<n; i++) q_arr[2*i]=q_arr[2*i+1] = w_arr[i];
140: VecRestoreArray(q,&q_arr);
141: VecRestoreArray(user->work1,&w_arr);
142: PetscLogEventEnd(event_update_q,0,0,0,0);
143: return(0);
144: }
148: PetscErrorCode SetInitialGuess(Vec X,AppCtx *user)
149: {
151: PetscScalar *x,*u;
152: PetscInt n,i;
153: Vec rand;
156: /* u = -0.4 + 0.05*rand(N,1)*(rand(N,1) - 0.5) */
157: VecDuplicate(user->u,&rand);
158: VecSetRandom(rand,NULL);
159: VecCopy(rand,user->u);
160: VecShift(rand,-0.5);
161: VecPointwiseMult(user->u,user->u,rand);
162: VecDestroy(&rand);
163: VecScale(user->u,0.05);
164: VecShift(user->u,-0.4);
166: VecGetLocalSize(X,&n);
167: VecGetArray(X,&x);
168: VecGetArray(user->u,&u);
169: /* Set initial guess, only set value for 2nd dof */
170: for (i=0; i<n/2; i++) x[2*i+1] = u[i];
171: VecRestoreArray(X,&x);
172: VecRestoreArray(user->u,&u);
173: return(0);
174: }
178: PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ctx)
179: {
181: AppCtx *user=(AppCtx*)ctx;
184: MatMultAdd(user->M,X,user->q,F);
185: return(0);
186: }
190: PetscErrorCode FormJacobian(SNES snes,Vec X,Mat J,Mat B,void *ctx)
191: {
192: PetscErrorCode ierr;
193: AppCtx *user =(AppCtx*)ctx;
194: static PetscBool copied = PETSC_FALSE;
197: /* for active set method the matrix does not get changed, so do not need to copy each time,
198: if the active set remains the same for several solves the preconditioner does not need to be rebuilt*/
199: if (!copied) {
200: MatCopy(user->M,J,SAME_NONZERO_PATTERN);
201: copied = PETSC_TRUE;
202: }
203: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
204: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
205: return(0);
206: }
209: PetscErrorCode SetVariableBounds(DM da,Vec xl,Vec xu)
210: {
212: PetscScalar ***l,***u;
213: PetscInt xs,xm,ys,ym;
214: PetscInt j,i;
217: DMDAVecGetArrayDOF(da,xl,&l);
218: DMDAVecGetArrayDOF(da,xu,&u);
220: DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);
222: for (j=ys; j < ys+ym; j++) {
223: for (i=xs; i < xs+xm;i++) {
224: l[j][i][0] = -PETSC_INFINITY;
225: l[j][i][1] = -1.0;
226: u[j][i][0] = PETSC_INFINITY;
227: u[j][i][1] = 1.0;
228: }
229: }
231: DMDAVecRestoreArrayDOF(da,xl,&l);
232: DMDAVecRestoreArrayDOF(da,xu,&u);
233: return(0);
234: }
238: PetscErrorCode GetParams(AppCtx *user)
239: {
241: PetscBool flg;
244: /* Set default parameters */
245: user->tsmonitor = PETSC_FALSE;
246: user->xmin = 0.0; user->xmax = 1.0;
247: user->ymin = 0.0; user->ymax = 1.0;
248: user->T = 0.0002; user->dt = 0.0001;
249: user->gamma = 3.2E-4; user->theta_c = 0;
251: PetscOptionsGetBool(NULL,"-ts_monitor",&user->tsmonitor,NULL);
252: PetscOptionsGetReal(NULL,"-xmin",&user->xmin,&flg);
253: PetscOptionsGetReal(NULL,"-xmax",&user->xmax,&flg);
254: PetscOptionsGetReal(NULL,"-ymin",&user->ymin,&flg);
255: PetscOptionsGetReal(NULL,"-ymax",&user->ymax,&flg);
256: PetscOptionsGetReal(NULL,"-T",&user->T,&flg);
257: PetscOptionsGetReal(NULL,"-dt",&user->dt,&flg);
258: PetscOptionsGetScalar(NULL,"-gamma",&user->gamma,&flg);
259: PetscOptionsGetScalar(NULL,"-theta_c",&user->theta_c,&flg);
260: return(0);
261: }
263: static void Gausspoints(PetscScalar *xx,PetscScalar *yy,PetscScalar *w,PetscScalar *x,PetscScalar *y)
264: {
266: xx[0] = 2.0/3.0*x[0] + 1.0/6.0*x[1] + 1.0/6.0*x[2];
267: xx[1] = 1.0/6.0*x[0] + 2.0/3.0*x[1] + 1.0/6.0*x[2];
268: xx[2] = 1.0/6.0*x[0] + 1.0/6.0*x[1] + 2.0/3.0*x[2];
270: yy[0] = 2.0/3.0*y[0] + 1.0/6.0*y[1] + 1.0/6.0*y[2];
271: yy[1] = 1.0/6.0*y[0] + 2.0/3.0*y[1] + 1.0/6.0*y[2];
272: yy[2] = 1.0/6.0*y[0] + 1.0/6.0*y[1] + 2.0/3.0*y[2];
274: *w = PetscAbsScalar(x[0]*(y[2]-y[1]) + x[2]*(y[1]-y[0]) + x[1]*(y[0]-y[2]))/6.0;
276: }
278: static void ShapefunctionsT3(PetscScalar *phi,PetscScalar phider[][2],PetscScalar xx,PetscScalar yy,PetscScalar *x,PetscScalar *y)
279: {
280: PetscScalar area,a1,a2,a3,b1,b2,b3,c1,c2,c3,pp;
282: /* Area of the triangle */
283: area = 1.0/2.0*PetscAbsScalar(x[0]*(y[2]-y[1]) + x[2]*(y[1]-y[0]) + x[1]*(y[0]-y[2]));
285: a1 = x[1]*y[2]-x[2]*y[1]; a2 = x[2]*y[0]-x[0]*y[2]; a3 = x[0]*y[1]-x[1]*y[0];
286: b1 = y[1]-y[2]; b2 = y[2]-y[0]; b3 = y[0]-y[1];
287: c1 = x[2]-x[1]; c2 = x[0]-x[2]; c3 = x[1]-x[0];
288: pp = 1.0/(2.0*area);
290: /* shape functions */
291: phi[0] = pp*(a1 + b1*xx + c1*yy);
292: phi[1] = pp*(a2 + b2*xx + c2*yy);
293: phi[2] = pp*(a3 + b3*xx + c3*yy);
295: /* shape functions derivatives */
296: phider[0][0] = pp*b1; phider[0][1] = pp*c1;
297: phider[1][0] = pp*b2; phider[1][1] = pp*c2;
298: phider[2][0] = pp*b3; phider[2][1] = pp*c3;
300: }
304: PetscErrorCode SetUpMatrices(AppCtx *user)
305: {
306: PetscErrorCode ierr;
307: PetscInt nele,nen,i;
308: const PetscInt *ele;
309: PetscScalar dt=user->dt;
310: Vec coords;
311: const PetscScalar *_coords;
312: PetscScalar x[3],y[3],xx[3],yy[3],w;
313: PetscInt idx[3];
314: PetscScalar phi[3],phider[3][2];
315: PetscScalar eM_0[3][3],eM_2[3][3];
316: Mat M =user->M;
317: PetscScalar gamma=user->gamma,theta_c=user->theta_c;
318: PetscInt m;
319: PetscInt j,k;
320: PetscInt row,cols[6],r;
321: PetscScalar vals[6];
322: PetscInt n,rstart;
323: IS isrow,iscol;
326: /* Get ghosted coordinates */
327: DMGetCoordinatesLocal(user->da,&coords);
328: VecGetArrayRead(coords,&_coords);
330: /* Get local element info */
331: DMDAGetElements(user->da,&nele,&nen,&ele);
332: for (i=0; i < nele; i++) {
333: idx[0] = ele[3*i]; idx[1] = ele[3*i+1]; idx[2] = ele[3*i+2];
334: x[0] = _coords[2*idx[0]]; y[0] = _coords[2*idx[0]+1];
335: x[1] = _coords[2*idx[1]]; y[1] = _coords[2*idx[1]+1];
336: x[2] = _coords[2*idx[2]]; y[2] = _coords[2*idx[2]+1];
338: PetscMemzero(xx,3*sizeof(PetscScalar));
339: PetscMemzero(yy,3*sizeof(PetscScalar));
340: Gausspoints(xx,yy,&w,x,y);
342: eM_0[0][0]=eM_0[0][1]=eM_0[0][2]=0.0;
343: eM_0[1][0]=eM_0[1][1]=eM_0[1][2]=0.0;
344: eM_0[2][0]=eM_0[2][1]=eM_0[2][2]=0.0;
345: eM_2[0][0]=eM_2[0][1]=eM_2[0][2]=0.0;
346: eM_2[1][0]=eM_2[1][1]=eM_2[1][2]=0.0;
347: eM_2[2][0]=eM_2[2][1]=eM_2[2][2]=0.0;
350: for (m=0; m<3; m++) {
351: PetscMemzero(phi,3*sizeof(PetscScalar));
352: phider[0][0]=phider[0][1]=0.0;
353: phider[1][0]=phider[1][1]=0.0;
354: phider[2][0]=phider[2][1]=0.0;
356: ShapefunctionsT3(phi,phider,xx[m],yy[m],x,y);
358: for (j=0; j<3; j++) {
359: for (k=0; k<3; k++) {
360: eM_0[k][j] += phi[j]*phi[k]*w;
361: eM_2[k][j] += phider[j][0]*phider[k][0]*w + phider[j][1]*phider[k][1]*w;
362: }
363: }
364: }
366: for (r=0; r<3; r++) {
367: row = 2*idx[r];
368: cols[0] = 2*idx[0]; vals[0] = dt*eM_2[r][0];
369: cols[1] = 2*idx[0]+1; vals[1] = eM_0[r][0];
370: cols[2] = 2*idx[1]; vals[2] = dt*eM_2[r][1];
371: cols[3] = 2*idx[1]+1; vals[3] = eM_0[r][1];
372: cols[4] = 2*idx[2]; vals[4] = dt*eM_2[r][2];
373: cols[5] = 2*idx[2]+1; vals[5] = eM_0[r][2];
375: /* Insert values in matrix M for 1st dof */
376: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
377: row = 2*idx[r]+1;
378: cols[0] = 2*idx[0]; vals[0] = -eM_0[r][0];
379: cols[1] = 2*idx[0]+1; vals[1] = gamma*eM_2[r][0]-theta_c*eM_0[r][0];
380: cols[2] = 2*idx[1]; vals[2] = -eM_0[r][1];
381: cols[3] = 2*idx[1]+1; vals[3] = gamma*eM_2[r][1]-theta_c*eM_0[r][1];
382: cols[4] = 2*idx[2]; vals[4] = -eM_0[r][2];
383: cols[5] = 2*idx[2]+1; vals[5] = gamma*eM_2[r][2]-theta_c*eM_2[r][2];
385: /* Insert values in matrix M for 2nd dof */
386: MatSetValuesLocal(M,1,&row,6,cols,vals,ADD_VALUES);
387: }
388: }
390: DMDARestoreElements(user->da,&nele,&nen,&ele);
391: VecRestoreArrayRead(coords,&_coords);
393: MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
394: MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);
396: /* Create ISs to extract matrix M_0 from M */
398: MatGetLocalSize(M,&n,NULL);
399: MatGetOwnershipRange(M,&rstart,NULL);
400: ISCreateStride(PETSC_COMM_WORLD,n/2,rstart,2,&isrow);
401: ISCreateStride(PETSC_COMM_WORLD,n/2,rstart+1,2,&iscol);
403: /* Extract M_0 from M */
404: MatGetSubMatrix(M,isrow,iscol,MAT_INITIAL_MATRIX,&user->M_0);
405: VecCreate(PETSC_COMM_WORLD,&user->u);
406: VecSetSizes(user->u,n/2,PETSC_DECIDE);
407: VecSetFromOptions(user->u);
408: VecDuplicate(user->u,&user->work1);
409: ISDestroy(&isrow);
410: ISDestroy(&iscol);
411: return(0);
412: }