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;
36: VecGetArrayRead(X,&x);
37: VecGetArrayRead(Xdot,&xdot);
38: 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: VecRestoreArrayRead(X,&x);
42: VecRestoreArrayRead(Xdot,&xdot);
43: VecRestoreArray(F,&f);
44: return 0;
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];
55: VecGetArrayRead(X,&x);
56: J[0][0] = a; J[0][1] = -1.0;
57: 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]);
58: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
59: VecRestoreArrayRead(X,&x);
61: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
62: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
63: if (A != B) {
64: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
65: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
66: }
67: return 0;
68: }
70: int main(int argc,char **argv)
71: {
72: TS ts; /* nonlinear solver */
73: Vec x; /* solution, residual vectors */
74: Mat A; /* Jacobian matrix */
75: PetscInt steps;
76: PetscReal ftime = 2;
77: PetscScalar *x_ptr;
78: PetscMPIInt size;
79: struct _n_User user;
82: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83: Initialize program
84: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85: PetscInitialize(&argc,&argv,NULL,help);
86: MPI_Comm_size(PETSC_COMM_WORLD,&size);
89: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
90: Set runtime options
91: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
92: user.next_output = 0.0;
93: user.mu = 1.0e6;
94: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
95: PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);
96: PetscOptionsEnd();
98: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
99: Create necessary matrix and vectors, solve same ODE on every process
100: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101: MatCreate(PETSC_COMM_WORLD,&A);
102: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
103: MatSetFromOptions(A);
104: MatSetUp(A);
106: MatCreateVecs(A,&x,NULL);
108: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109: Create timestepping solver context
110: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111: TSCreate(PETSC_COMM_WORLD,&ts);
112: TSSetType(ts,TSBEULER);
113: TSSetIFunction(ts,NULL,IFunction,&user);
114: TSSetIJacobian(ts,A,A,IJacobian,&user);
116: TSSetMaxTime(ts,ftime);
117: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
118: TSSetTolerances(ts,1.e-4,NULL,1.e-4,NULL);
119: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120: Set initial conditions
121: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
122: VecGetArray(x,&x_ptr);
123: x_ptr[0] = 2.0; x_ptr[1] = -6.6e-01;
124: VecRestoreArray(x,&x_ptr);
125: TSSetTimeStep(ts,.000001);
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Set runtime options
129: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130: TSSetFromOptions(ts);
132: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133: Solve nonlinear system
134: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135: TSSolve(ts,x);
136: TSGetSolveTime(ts,&ftime);
137: TSGetStepNumber(ts,&steps);
138: PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);
139: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
141: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: Free work space. All PETSc objects should be destroyed when they
143: are no longer needed.
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145: MatDestroy(&A);
146: VecDestroy(&x);
147: TSDestroy(&ts);
149: PetscFinalize();
150: return(ierr);
151: }
153: /*TEST
155: build:
156: requires: double !complex !defined(PETSC_USE_64BIT_INDICES) radau5
158: test:
159: args: -ts_monitor_solution -ts_type radau5
161: TEST*/