Actual source code: ex20.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) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2),
12: and
13: \mu = 10^6 ( y'(0) ~ -0.6666665432100101).
14: 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.
16: Notes:
17: This code demonstrates the TS solver interface to an ODE -- RHSFunction for explicit form and IFunction for implicit form.
19: ------------------------------------------------------------------------- */
21: #include <petscts.h>
23: typedef struct _n_User *User;
24: struct _n_User {
25: PetscReal mu;
26: PetscReal next_output;
27: };
29: /*
30: User-defined routines
31: */
32: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx)
33: {
34: User user = (User)ctx;
35: PetscScalar *f;
36: const PetscScalar *x;
39: VecGetArrayRead(X,&x);
40: VecGetArray(F,&f);
41: f[0] = x[1];
42: f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0];
43: VecRestoreArrayRead(X,&x);
44: VecRestoreArray(F,&f);
45: return 0;
46: }
48: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
49: {
50: User user = (User)ctx;
51: const PetscScalar *x,*xdot;
52: PetscScalar *f;
55: VecGetArrayRead(X,&x);
56: VecGetArrayRead(Xdot,&xdot);
57: VecGetArray(F,&f);
58: f[0] = xdot[0] - x[1];
59: f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]);
60: VecRestoreArrayRead(X,&x);
61: VecRestoreArrayRead(Xdot,&xdot);
62: VecRestoreArray(F,&f);
63: return 0;
64: }
66: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
67: {
68: User user = (User)ctx;
69: PetscInt rowcol[] = {0,1};
70: const PetscScalar *x;
71: PetscScalar J[2][2];
74: VecGetArrayRead(X,&x);
75: J[0][0] = a; J[0][1] = -1.0;
76: 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]);
77: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
78: VecRestoreArrayRead(X,&x);
80: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
81: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
82: if (A != B) {
83: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
84: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
85: }
86: return 0;
87: }
89: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
90: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
91: {
92: PetscErrorCode ierr;
93: const PetscScalar *x;
94: PetscReal tfinal, dt;
95: User user = (User)ctx;
96: Vec interpolatedX;
99: TSGetTimeStep(ts,&dt);
100: TSGetMaxTime(ts,&tfinal);
102: while (user->next_output <= t && user->next_output <= tfinal) {
103: VecDuplicate(X,&interpolatedX);
104: TSInterpolate(ts,user->next_output,interpolatedX);
105: VecGetArrayRead(interpolatedX,&x);
106: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
107: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
108: (double)PetscRealPart(x[1]));
109: VecRestoreArrayRead(interpolatedX,&x);
110: VecDestroy(&interpolatedX);
111: user->next_output += 0.1;
112: }
113: return 0;
114: }
116: int main(int argc,char **argv)
117: {
118: TS ts; /* nonlinear solver */
119: Vec x; /* solution, residual vectors */
120: Mat A; /* Jacobian matrix */
121: PetscInt steps;
122: PetscReal ftime = 0.5;
123: PetscBool monitor = PETSC_FALSE,implicitform = PETSC_TRUE;
124: PetscScalar *x_ptr;
125: PetscMPIInt size;
126: struct _n_User user;
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Initialize program
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132: PetscInitialize(&argc,&argv,NULL,help);
133: MPI_Comm_size(PETSC_COMM_WORLD,&size);
136: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: Set runtime options
138: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
139: user.next_output = 0.0;
140: user.mu = 1.0e3;
141: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
142: PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL);
143: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
144: PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);
145: PetscOptionsEnd();
147: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: Create necessary matrix and vectors, solve same ODE on every process
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: MatCreate(PETSC_COMM_WORLD,&A);
151: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
152: MatSetFromOptions(A);
153: MatSetUp(A);
155: MatCreateVecs(A,&x,NULL);
157: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158: Create timestepping solver context
159: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160: TSCreate(PETSC_COMM_WORLD,&ts);
161: if (implicitform) {
162: TSSetIFunction(ts,NULL,IFunction,&user);
163: TSSetIJacobian(ts,A,A,IJacobian,&user);
164: TSSetType(ts,TSBEULER);
165: } else {
166: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
167: TSSetType(ts,TSRK);
168: }
169: TSSetMaxTime(ts,ftime);
170: TSSetTimeStep(ts,0.001);
171: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
172: if (monitor) {
173: TSMonitorSet(ts,Monitor,&user,NULL);
174: }
176: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: Set initial conditions
178: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
179: VecGetArray(x,&x_ptr);
180: x_ptr[0] = 2.0;
181: x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu);
182: VecRestoreArray(x,&x_ptr);
184: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Set runtime options
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
187: TSSetFromOptions(ts);
189: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: Solve nonlinear system
191: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
192: TSSolve(ts,x);
193: TSGetSolveTime(ts,&ftime);
194: TSGetStepNumber(ts,&steps);
195: PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);
196: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Free work space. All PETSc objects should be destroyed when they
200: are no longer needed.
201: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
202: MatDestroy(&A);
203: VecDestroy(&x);
204: TSDestroy(&ts);
206: PetscFinalize();
207: return(ierr);
208: }
210: /*TEST
212: test:
213: requires: !single
214: args: -mu 1e6
216: test:
217: requires: !single
218: suffix: 2
219: args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp
221: test:
222: requires: !single
223: suffix: 3
224: args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312
226: TEST*/