Actual source code: ex49.c


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

  5: /* ------------------------------------------------------------------------

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

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

 19:   ------------------------------------------------------------------------- */

 21: #include <petscts.h>

 23: typedef struct _n_User *User;
 24: struct _n_User {
 25:   PetscReal mu;
 26:   PetscReal next_output;
 27: };

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

 35:   PetscFunctionBeginUser;
 36:   PetscCall(VecGetArrayRead(X, &x));
 37:   PetscCall(VecGetArrayRead(Xdot, &xdot));
 38:   PetscCall(VecGetArray(F, &f));
 39:   f[0] = xdot[0] - x[1];
 40:   f[1] = xdot[1] - user->mu * ((1.0 - x[0] * x[0]) * x[1] - x[0]);
 41:   PetscCall(VecRestoreArrayRead(X, &x));
 42:   PetscCall(VecRestoreArrayRead(Xdot, &xdot));
 43:   PetscCall(VecRestoreArray(F, &f));
 44:   PetscFunctionReturn(PETSC_SUCCESS);
 45: }

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

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

 63:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
 64:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
 65:   if (A != B) {
 66:     PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
 67:     PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
 68:   }
 69:   PetscFunctionReturn(PETSC_SUCCESS);
 70: }

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

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

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

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

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

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

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

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

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

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

152:   PetscCall(PetscFinalize());
153:   return (0);
154: }

156: /*TEST

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

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

164: TEST*/