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*/