Actual source code: ex49.c

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

      4: /* ------------------------------------------------------------------------

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

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

     18:   ------------------------------------------------------------------------- */

     20: #include <petscts.h>

     22: typedef struct _n_User *User;
     23: struct _n_User {
     24:   PetscReal mu;
     25:   PetscReal next_output;
     26: };

     28: static PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, void *ctx)
     29: {
     30:   User               user = (User)ctx;
     31:   const PetscScalar *x, *xdot;
     32:   PetscScalar       *f;

     34:   PetscFunctionBeginUser;
     35:   PetscCall(VecGetArrayRead(X, &x));
     36:   PetscCall(VecGetArrayRead(Xdot, &xdot));
     37:   PetscCall(VecGetArray(F, &f));
     38:   f[0] = xdot[0] - x[1];
     39:   f[1] = xdot[1] - user->mu * ((1.0 - x[0] * x[0]) * x[1] - x[0]);
     40:   PetscCall(VecRestoreArrayRead(X, &x));
     41:   PetscCall(VecRestoreArrayRead(Xdot, &xdot));
     42:   PetscCall(VecRestoreArray(F, &f));
     43:   PetscFunctionReturn(PETSC_SUCCESS);
     44: }

     46: static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat A, Mat B, void *ctx)
     47: {
     48:   User               user     = (User)ctx;
     49:   PetscInt           rowcol[] = {0, 1};
     50:   const PetscScalar *x;
     51:   PetscScalar        J[2][2];

     53:   PetscFunctionBeginUser;
     54:   PetscCall(VecGetArrayRead(X, &x));
     55:   J[0][0] = a;
     56:   J[0][1] = -1.0;
     57:   J[1][0] = user->mu * (1.0 + 2.0 * x[0] * x[1]);
     58:   J[1][1] = a - user->mu * (1.0 - x[0] * x[0]);
     59:   PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
     60:   PetscCall(VecRestoreArrayRead(X, &x));

     62:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
     63:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
     64:   if (A != B) {
     65:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
     66:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
     67:   }
     68:   PetscFunctionReturn(PETSC_SUCCESS);
     69: }

     71: int main(int argc, char **argv)
     72: {
     73:   TS             ts; /* nonlinear solver */
     74:   Vec            x;  /* solution, residual vectors */
     75:   Mat            A;  /* Jacobian matrix */
     76:   PetscInt       steps;
     77:   PetscReal      ftime = 2;
     78:   PetscScalar   *x_ptr;
     79:   PetscMPIInt    size;
     80:   struct _n_User user;

     82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     83:      Initialize program
     84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     85:   PetscFunctionBeginUser;
     86:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
     87:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
     88:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");

     90:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     91:     Set runtime options
     92:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     93:   user.next_output = 0.0;
     94:   user.mu          = 1.0e6;
     95:   PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Physical parameters", NULL);
     96:   PetscCall(PetscOptionsReal("-mu", "Stiffness parameter", "<1.0e6>", user.mu, &user.mu, NULL));
     97:   PetscOptionsEnd();

     99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    100:     Create necessary matrix and vectors, solve same ODE on every process
    101:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    102:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
    103:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, 2, 2));
    104:   PetscCall(MatSetFromOptions(A));
    105:   PetscCall(MatSetUp(A));

    107:   PetscCall(MatCreateVecs(A, &x, NULL));

    109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    110:      Create timestepping solver context
    111:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    112:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
    113:   PetscCall(TSSetType(ts, TSBEULER));
    114:   PetscCall(TSSetIFunction(ts, NULL, IFunction, &user));
    115:   PetscCall(TSSetIJacobian(ts, A, A, IJacobian, &user));

    117:   PetscCall(TSSetMaxTime(ts, ftime));
    118:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
    119:   PetscCall(TSSetTolerances(ts, 1.e-4, NULL, 1.e-4, NULL));
    120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    121:      Set initial conditions
    122:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    123:   PetscCall(VecGetArray(x, &x_ptr));
    124:   x_ptr[0] = 2.0;
    125:   x_ptr[1] = -6.6e-01;
    126:   PetscCall(VecRestoreArray(x, &x_ptr));
    127:   PetscCall(TSSetTimeStep(ts, .000001));

    129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    130:      Set runtime options
    131:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    132:   PetscCall(TSSetFromOptions(ts));

    134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    135:      Solve nonlinear system
    136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    137:   PetscCall(TSSolve(ts, x));
    138:   PetscCall(TSGetSolveTime(ts, &ftime));
    139:   PetscCall(TSGetStepNumber(ts, &steps));
    140:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "steps %" PetscInt_FMT ", ftime %g\n", steps, (double)ftime));
    141:   PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD));

    143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    144:      Free work space.  All PETSc objects should be destroyed when they
    145:      are no longer needed.
    146:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    147:   PetscCall(MatDestroy(&A));
    148:   PetscCall(VecDestroy(&x));
    149:   PetscCall(TSDestroy(&ts));

    151:   PetscCall(PetscFinalize());
    152:   return 0;
    153: }

    155: /*TEST

    157:     build:
    158:       requires: double !complex !defined(PETSC_USE_64BIT_INDICES) radau5

    160:     test:
    161:       args: -ts_monitor_solution -ts_type radau5

    163: TEST*/