Actual source code: ex20.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) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2),
17: and
18: \mu = 10^6 ( y'(0) ~ -0.6666665432100101).
19: This is a nonlinear equation. The well prepared initial condition gives errors that are not dominated by the first few steps of the method when \mu is large.
21: Notes:
22: This code demonstrates the TS solver interface to an ODE -- RHSFunction for explicit form and IFunction for implicit form.
24: ------------------------------------------------------------------------- */
26: #include <petscts.h>
28: typedef struct _n_User *User;
29: struct _n_User {
30: PetscReal mu;
31: PetscReal next_output;
32: };
34: /*
35: User-defined routines
36: */
37: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx)
38: {
39: User user = (User)ctx;
40: PetscScalar *f;
41: const PetscScalar *x;
44: VecGetArrayRead(X,&x);
45: VecGetArray(F,&f);
46: f[0] = x[1];
47: f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0];
48: VecRestoreArrayRead(X,&x);
49: VecRestoreArray(F,&f);
50: return 0;
51: }
53: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
54: {
55: User user = (User)ctx;
56: const PetscScalar *x,*xdot;
57: PetscScalar *f;
60: VecGetArrayRead(X,&x);
61: VecGetArrayRead(Xdot,&xdot);
62: VecGetArray(F,&f);
63: f[0] = xdot[0] - x[1];
64: f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]);
65: VecRestoreArrayRead(X,&x);
66: VecRestoreArrayRead(Xdot,&xdot);
67: VecRestoreArray(F,&f);
68: return 0;
69: }
71: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
72: {
73: User user = (User)ctx;
74: PetscInt rowcol[] = {0,1};
75: const PetscScalar *x;
76: PetscScalar J[2][2];
79: VecGetArrayRead(X,&x);
80: J[0][0] = a; J[0][1] = -1.0;
81: J[1][0] = user->mu*(2.0*x[0]*x[1] + 1.0); J[1][1] = a - user->mu*(1.0-x[0]*x[0]);
82: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
83: VecRestoreArrayRead(X,&x);
85: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
86: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
87: if (A != B) {
88: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
89: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
90: }
91: return 0;
92: }
94: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
95: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
96: {
97: PetscErrorCode ierr;
98: const PetscScalar *x;
99: PetscReal tfinal, dt;
100: User user = (User)ctx;
101: Vec interpolatedX;
104: TSGetTimeStep(ts,&dt);
105: TSGetMaxTime(ts,&tfinal);
107: while (user->next_output <= t && user->next_output <= tfinal) {
108: VecDuplicate(X,&interpolatedX);
109: TSInterpolate(ts,user->next_output,interpolatedX);
110: VecGetArrayRead(interpolatedX,&x);
111: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
112: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
113: (double)PetscRealPart(x[1]));
114: VecRestoreArrayRead(interpolatedX,&x);
115: VecDestroy(&interpolatedX);
116: user->next_output += 0.1;
117: }
118: return 0;
119: }
121: int main(int argc,char **argv)
122: {
123: TS ts; /* nonlinear solver */
124: Vec x; /* solution, residual vectors */
125: Mat A; /* Jacobian matrix */
126: PetscInt steps;
127: PetscReal ftime = 0.5;
128: PetscBool monitor = PETSC_FALSE,implicitform = PETSC_TRUE;
129: PetscScalar *x_ptr;
130: PetscMPIInt size;
131: struct _n_User user;
134: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135: Initialize program
136: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137: PetscInitialize(&argc,&argv,NULL,help);
138: MPI_Comm_size(PETSC_COMM_WORLD,&size);
141: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: Set runtime options
143: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144: user.next_output = 0.0;
145: user.mu = 1.0e3;
146: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
147: PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL);
148: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
149: PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);
150: PetscOptionsEnd();
152: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: Create necessary matrix and vectors, solve same ODE on every process
154: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155: MatCreate(PETSC_COMM_WORLD,&A);
156: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
157: MatSetFromOptions(A);
158: MatSetUp(A);
160: MatCreateVecs(A,&x,NULL);
162: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: Create timestepping solver context
164: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
165: TSCreate(PETSC_COMM_WORLD,&ts);
166: if (implicitform) {
167: TSSetIFunction(ts,NULL,IFunction,&user);
168: TSSetIJacobian(ts,A,A,IJacobian,&user);
169: TSSetType(ts,TSBEULER);
170: } else {
171: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
172: TSSetType(ts,TSRK);
173: }
174: TSSetMaxTime(ts,ftime);
175: TSSetTimeStep(ts,0.001);
176: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
177: if (monitor) {
178: TSMonitorSet(ts,Monitor,&user,NULL);
179: }
181: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
182: Set initial conditions
183: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
184: VecGetArray(x,&x_ptr);
185: x_ptr[0] = 2.0;
186: x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu);
187: VecRestoreArray(x,&x_ptr);
189: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: Set runtime options
191: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
192: TSSetFromOptions(ts);
194: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195: Solve nonlinear system
196: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
197: TSSolve(ts,x);
198: TSGetSolveTime(ts,&ftime);
199: TSGetStepNumber(ts,&steps);
200: PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);
201: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
203: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204: Free work space. All PETSc objects should be destroyed when they
205: are no longer needed.
206: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
207: MatDestroy(&A);
208: VecDestroy(&x);
209: TSDestroy(&ts);
211: PetscFinalize();
212: return(ierr);
213: }
215: /*TEST
217: test:
218: requires: !single
219: args: -mu 1e6
221: test:
222: requires: !single
223: suffix: 2
224: args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp
226: test:
227: requires: !single
228: suffix: 3
229: args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312
231: TEST*/