Actual source code: allen_cahn.c

petsc-3.6.4 2016-04-12
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  1: static char help[] ="Solves the time dependent Allen-Cahn equation with IMEX methods";

  3: /*
  4:  * allen_cahn.c
  5:  *
  6:  *  Created on: Jun 8, 2012
  7:  *      Author: Hong Zhang
  8:  */

 10: #include <petscts.h>

 12: /*
 13:  * application context
 14:  */
 15: typedef struct {
 16:   PetscReal   param;        /* parameter */
 17:   PetscReal   xleft,xright;  /* range in x-direction */
 18:   PetscInt    mx;           /* Discretization in x-direction */
 19: }AppCtx;


 22: static PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*);
 23: static PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*);
 24: static PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void *ctx);
 25: static PetscErrorCode FormInitialSolution(TS,Vec,void*);


 30: int main(int argc, char **argv)
 31: {
 32:   TS                ts;
 33:   Vec               x; /*solution vector*/
 34:   Mat               A; /*Jacobian*/
 35:   PetscInt          steps,maxsteps,mx;
 36:   PetscErrorCode    ierr;
 37:   PetscReal         ftime;
 38:   AppCtx      user;       /* user-defined work context */

 40:   PetscInitialize(&argc,&argv,NULL,help);

 42:   /* Initialize user application context */
 43:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Allen-Cahn equation","");
 44:   user.param = 9e-4;
 45:   user.xleft = -1.;
 46:   user.xright = 2.;
 47:   user.mx = 400;
 48:   PetscOptionsReal("-eps","parameter","",user.param,&user.param,NULL);
 49:   PetscOptionsEnd();

 51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 52:    Set runtime options
 53:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 54:   /*
 55:    * PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);
 56:    */
 57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 58:    Create necessary matrix and vectors, solve same ODE on every process
 59:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 60:   MatCreate(PETSC_COMM_WORLD,&A);
 61:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,user.mx,user.mx);
 62:   MatSetFromOptions(A);
 63:   MatSetUp(A);
 64:   MatCreateVecs(A,&x,NULL);

 66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 67:    Create time stepping solver context
 68:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 69:   TSCreate(PETSC_COMM_WORLD,&ts);
 70:   TSSetType(ts,TSEIMEX);
 71:   TSSetRHSFunction(ts,NULL,RHSFunction,&user);
 72:   TSSetIFunction(ts,NULL,FormIFunction,&user);
 73:   TSSetIJacobian(ts,A,A,FormIJacobian,&user);
 74:   ftime = 142;
 75:   maxsteps = 100000;
 76:   TSSetDuration(ts,maxsteps,ftime);

 78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 79:    Set initial conditions
 80:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 81:   FormInitialSolution(ts,x,&user);
 82:   TSSetSolution(ts,x);
 83:   VecGetSize(x,&mx);

 85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 86:    Set runtime options
 87:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 88:   TSSetFromOptions(ts);

 90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 91:    Solve nonlinear system
 92:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 93:   TSSolve(ts,x);
 94:   TSGetTime(ts,&ftime);
 95:   TSGetTimeStepNumber(ts,&steps);
 96:   PetscPrintf(PETSC_COMM_WORLD,"eps %g, steps %D, ftime %g\n",(double)user.param,steps,(double)ftime);
 97:   /*   VecView(x,PETSC_VIEWER_STDOUT_WORLD);*/

 99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100:    Free work space.
101:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
102:   MatDestroy(&A);
103:   VecDestroy(&x);
104:   TSDestroy(&ts);
105:   PetscFinalize();
106:   return(0);
107: }


112: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
113: {
114:   PetscErrorCode    ierr;
115:   AppCtx            *user = (AppCtx*)ptr;
116:   PetscScalar       *f;
117:   const PetscScalar *x;
118:   PetscInt          i,mx;
119:   PetscReal         hx,eps;

122:   mx = user->mx;
123:   eps = user->param;
124:   hx = (user->xright-user->xleft)/(mx-1);
125:   VecGetArrayRead(X,&x);
126:   VecGetArray(F,&f);
127:   f[0] = 2.*eps*(x[1]-x[0])/(hx*hx); /*boundary*/
128:   for(i=1;i<mx-1;i++) {
129:     f[i]= eps*(x[i+1]-2.*x[i]+x[i-1])/(hx*hx);
130:   }
131:   f[mx-1] = 2.*eps*(x[mx-2]- x[mx-1])/(hx*hx); /*boundary*/
132:   VecRestoreArrayRead(X,&x);
133:   VecRestoreArray(F,&f);
134:   return(0);
135: }


140: static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ptr)
141: {
142:   PetscErrorCode    ierr;
143:   AppCtx            *user = (AppCtx*)ptr;
144:   PetscScalar       *f;
145:   const PetscScalar *x,*xdot;
146:   PetscInt          i,mx;

149:   mx = user->mx;
150:   VecGetArrayRead(X,&x);
151:   VecGetArrayRead(Xdot,&xdot);
152:   VecGetArray(F,&f);

154:   for(i=0;i<mx;i++) {
155:     f[i]= xdot[i] - x[i]*(1.-x[i]*x[i]);
156:   }

158:   VecRestoreArrayRead(X,&x);
159:   VecRestoreArrayRead(Xdot,&xdot);
160:   VecRestoreArray(F,&f);
161:   return(0);
162: }


167: static PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U, Vec Udot, PetscReal a, Mat J,Mat Jpre,void *ctx)
168: {
169:   PetscErrorCode    ierr;
170:   AppCtx            *user = (AppCtx *)ctx;
171:   PetscScalar       v;
172:   const PetscScalar *x;
173:   PetscInt          i,col;

176:   VecGetArrayRead(U,&x);
177:   for(i=0; i < user->mx; i++) {
178:     v = a - 1. + 3.*x[i]*x[i];
179:     col = i;
180:     MatSetValues(J,1,&i,1,&col,&v,INSERT_VALUES);
181:   }
182:   VecRestoreArrayRead(U,&x);

184:   MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
185:   MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
186:   if (J != Jpre) {
187:     MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
188:     MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
189:   }
190:   /*  MatView(J,PETSC_VIEWER_STDOUT_WORLD);*/
191:   return(0);
192: }


197: static PetscErrorCode FormInitialSolution(TS ts,Vec U,void *ctx)
198: {
199:   AppCtx *user = (AppCtx*)ctx;
200:   PetscInt       i;
201:   PetscScalar    *x;
202:   PetscReal      hx,x_map;

206:   hx = (user->xright-user->xleft)/(PetscReal)(user->mx-1);
207:   VecGetArray(U,&x);
208:   for(i=0;i<user->mx;i++) {
209:     x_map = user->xleft + i*hx;
210:     if(x_map >= 0.7065) {
211:       x[i] = tanh((x_map-0.8)/(2.*PetscSqrtReal(user->param)));
212:     } else if(x_map >= 0.4865) {
213:       x[i] = tanh((0.613-x_map)/(2.*PetscSqrtReal(user->param)));
214:     } else if(x_map >= 0.28) {
215:       x[i] = tanh((x_map-0.36)/(2.*PetscSqrtReal(user->param)));
216:     } else if(x_map >= -0.7) {
217:       x[i] = tanh((0.2-x_map)/(2.*PetscSqrtReal(user->param)));
218:     } else if(x_map >= -1) {
219:       x[i] = tanh((x_map+0.9)/(2.*PetscSqrtReal(user->param)));
220:     }
221:   }
222:   VecRestoreArray(U,&x);
223:   return(0);
224: }