Actual source code: ex49.c

      2: static char help[] = "Solves the van der Pol equation.\n\
      3: Input parameters include:\n";

      5: /*
      6:    Concepts: TS^time-dependent nonlinear problems
      7:    Concepts: TS^van der Pol equation DAE equivalent
      8:    Processors: 1
      9: */
     10: /* ------------------------------------------------------------------------

     12:    This program solves the van der Pol DAE ODE equivalent
     13:        y' = z                 (1)
     14:        z' = mu[(1-y^2)z-y]
     15:    on the domain 0 <= x <= 1, with the boundary conditions
     16:        y(0) = 2, y'(0) = -6.6e-01,
     17:    and
     18:        mu = 10^6.
     19:    This is a nonlinear equation.

     21:    This is a copy and modification of ex20.c to exactly match a test
     22:    problem that comes with the Radau5 integrator package.

     24:   ------------------------------------------------------------------------- */

     26: #include <petscts.h>

     28: typedef struct _n_User *User;
     29: struct _n_User {
     30:   PetscReal mu;
     31:   PetscReal next_output;
     32: };

     35: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
     36: {
     37:   PetscErrorCode    ierr;
     38:   User              user = (User)ctx;
     39:   const PetscScalar *x,*xdot;
     40:   PetscScalar       *f;

     43:   VecGetArrayRead(X,&x);
     44:   VecGetArrayRead(Xdot,&xdot);
     45:   VecGetArray(F,&f);
     46:   f[0] = xdot[0] - x[1];
     47:   f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]);
     48:   VecRestoreArrayRead(X,&x);
     49:   VecRestoreArrayRead(Xdot,&xdot);
     50:   VecRestoreArray(F,&f);
     51:   return(0);
     52: }

     54: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
     55: {
     56:   PetscErrorCode    ierr;
     57:   User              user     = (User)ctx;
     58:   PetscInt          rowcol[] = {0,1};
     59:   const PetscScalar *x;
     60:   PetscScalar       J[2][2];

     63:   VecGetArrayRead(X,&x);
     64:   J[0][0] = a;     J[0][1] = -1.0;
     65:   J[1][0] = user->mu*(1.0 + 2.0*x[0]*x[1]);   J[1][1] = a - user->mu*(1.0-x[0]*x[0]);
     66:   MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
     67:   VecRestoreArrayRead(X,&x);

     69:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
     70:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
     71:   if (A != B) {
     72:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     73:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     74:   }
     75:   return(0);
     76: }

     79: int main(int argc,char **argv)
     80: {
     81:   TS             ts;            /* nonlinear solver */
     82:   Vec            x;             /* solution, residual vectors */
     83:   Mat            A;             /* Jacobian matrix */
     84:   PetscInt       steps;
     85:   PetscReal      ftime   = 2;
     86:   PetscScalar    *x_ptr;
     87:   PetscMPIInt    size;
     88:   struct _n_User user;

     91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     92:      Initialize program
     93:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     94:   PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
     95:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
     96:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");

     98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     99:     Set runtime options
    100:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    101:   user.next_output = 0.0;
    102:   user.mu          = 1.0e6;
    103:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
    104:   PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);
    105:   PetscOptionsEnd();

    107:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    108:     Create necessary matrix and vectors, solve same ODE on every process
    109:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    110:   MatCreate(PETSC_COMM_WORLD,&A);
    111:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
    112:   MatSetFromOptions(A);
    113:   MatSetUp(A);

    115:   MatCreateVecs(A,&x,NULL);

    117:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    118:      Create timestepping solver context
    119:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    120:   TSCreate(PETSC_COMM_WORLD,&ts);
    121:   TSSetType(ts,TSBEULER);
    122:   TSSetIFunction(ts,NULL,IFunction,&user);
    123:   TSSetIJacobian(ts,A,A,IJacobian,&user);

    125:   TSSetMaxTime(ts,ftime);
    126:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
    127:   TSSetTolerances(ts,1.e-4,NULL,1.e-4,NULL);
    128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    129:      Set initial conditions
    130:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    131:   VecGetArray(x,&x_ptr);
    132:   x_ptr[0] = 2.0;   x_ptr[1] = -6.6e-01;
    133:   VecRestoreArray(x,&x_ptr);
    134:   TSSetTimeStep(ts,.000001);

    136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    137:      Set runtime options
    138:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    139:   TSSetFromOptions(ts);

    141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    142:      Solve nonlinear system
    143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    144:   TSSolve(ts,x);
    145:   TSGetSolveTime(ts,&ftime);
    146:   TSGetStepNumber(ts,&steps);
    147:   PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);
    148:   VecView(x,PETSC_VIEWER_STDOUT_WORLD);

    150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    151:      Free work space.  All PETSc objects should be destroyed when they
    152:      are no longer needed.
    153:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    154:   MatDestroy(&A);
    155:   VecDestroy(&x);
    156:   TSDestroy(&ts);

    158:   PetscFinalize();
    159:   return(ierr);
    160: }

    162: /*TEST

    164:     build:
    165:       requires: double !complex !define(PETSC_USE_64BIT_INDICES) radau5

    167:     test:
    168:       args: -ts_monitor_solution -ts_type radau5

    170: TEST*/