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: };
34: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
35: {
36: User user = (User)ctx;
37: const PetscScalar *x,*xdot;
38: PetscScalar *f;
41: VecGetArrayRead(X,&x);
42: VecGetArrayRead(Xdot,&xdot);
43: VecGetArray(F,&f);
44: f[0] = xdot[0] - x[1];
45: f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]);
46: VecRestoreArrayRead(X,&x);
47: VecRestoreArrayRead(Xdot,&xdot);
48: VecRestoreArray(F,&f);
49: return 0;
50: }
52: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
53: {
54: User user = (User)ctx;
55: PetscInt rowcol[] = {0,1};
56: const PetscScalar *x;
57: PetscScalar J[2][2];
60: VecGetArrayRead(X,&x);
61: J[0][0] = a; J[0][1] = -1.0;
62: 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]);
63: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
64: VecRestoreArrayRead(X,&x);
66: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
67: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
68: if (A != B) {
69: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
70: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
71: }
72: return 0;
73: }
75: int main(int argc,char **argv)
76: {
77: TS ts; /* nonlinear solver */
78: Vec x; /* solution, residual vectors */
79: Mat A; /* Jacobian matrix */
80: PetscInt steps;
81: PetscReal ftime = 2;
82: PetscScalar *x_ptr;
83: PetscMPIInt size;
84: struct _n_User user;
87: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
88: Initialize program
89: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
90: PetscInitialize(&argc,&argv,NULL,help);
91: MPI_Comm_size(PETSC_COMM_WORLD,&size);
94: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
95: Set runtime options
96: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
97: user.next_output = 0.0;
98: user.mu = 1.0e6;
99: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
100: PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);
101: PetscOptionsEnd();
103: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104: Create necessary matrix and vectors, solve same ODE on every process
105: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
106: MatCreate(PETSC_COMM_WORLD,&A);
107: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
108: MatSetFromOptions(A);
109: MatSetUp(A);
111: MatCreateVecs(A,&x,NULL);
113: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: Create timestepping solver context
115: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116: TSCreate(PETSC_COMM_WORLD,&ts);
117: TSSetType(ts,TSBEULER);
118: TSSetIFunction(ts,NULL,IFunction,&user);
119: TSSetIJacobian(ts,A,A,IJacobian,&user);
121: TSSetMaxTime(ts,ftime);
122: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
123: TSSetTolerances(ts,1.e-4,NULL,1.e-4,NULL);
124: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Set initial conditions
126: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
127: VecGetArray(x,&x_ptr);
128: x_ptr[0] = 2.0; x_ptr[1] = -6.6e-01;
129: VecRestoreArray(x,&x_ptr);
130: TSSetTimeStep(ts,.000001);
132: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133: Set runtime options
134: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135: TSSetFromOptions(ts);
137: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138: Solve nonlinear system
139: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
140: TSSolve(ts,x);
141: TSGetSolveTime(ts,&ftime);
142: TSGetStepNumber(ts,&steps);
143: PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);
144: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
146: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: Free work space. All PETSc objects should be destroyed when they
148: are no longer needed.
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: MatDestroy(&A);
151: VecDestroy(&x);
152: TSDestroy(&ts);
154: PetscFinalize();
155: return(ierr);
156: }
158: /*TEST
160: build:
161: requires: double !complex !defined(PETSC_USE_64BIT_INDICES) radau5
163: test:
164: args: -ts_monitor_solution -ts_type radau5
166: TEST*/