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: PetscErrorCode ierr;
40: User user = (User)ctx;
41: PetscScalar *f;
42: const PetscScalar *x;
45: VecGetArrayRead(X,&x);
46: VecGetArray(F,&f);
47: f[0] = x[1];
48: f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0];
49: VecRestoreArrayRead(X,&x);
50: VecRestoreArray(F,&f);
51: return(0);
52: }
54: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
55: {
56: PetscErrorCode ierr;
57: User user = (User)ctx;
58: const PetscScalar *x,*xdot;
59: PetscScalar *f;
62: VecGetArrayRead(X,&x);
63: VecGetArrayRead(Xdot,&xdot);
64: VecGetArray(F,&f);
65: f[0] = xdot[0] - x[1];
66: f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]);
67: VecRestoreArrayRead(X,&x);
68: VecRestoreArrayRead(Xdot,&xdot);
69: VecRestoreArray(F,&f);
70: return(0);
71: }
73: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
74: {
75: PetscErrorCode ierr;
76: User user = (User)ctx;
77: PetscInt rowcol[] = {0,1};
78: const PetscScalar *x;
79: PetscScalar J[2][2];
82: VecGetArrayRead(X,&x);
83: J[0][0] = a; J[0][1] = -1.0;
84: 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]);
85: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
86: VecRestoreArrayRead(X,&x);
88: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
89: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
90: if (A != B) {
91: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
92: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
93: }
94: return(0);
95: }
97: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
98: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
99: {
100: PetscErrorCode ierr;
101: const PetscScalar *x;
102: PetscReal tfinal, dt;
103: User user = (User)ctx;
104: Vec interpolatedX;
107: TSGetTimeStep(ts,&dt);
108: TSGetMaxTime(ts,&tfinal);
110: while (user->next_output <= t && user->next_output <= tfinal) {
111: VecDuplicate(X,&interpolatedX);
112: TSInterpolate(ts,user->next_output,interpolatedX);
113: VecGetArrayRead(interpolatedX,&x);
114: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
115: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
116: (double)PetscRealPart(x[1]));
117: VecRestoreArrayRead(interpolatedX,&x);
118: VecDestroy(&interpolatedX);
119: user->next_output += 0.1;
120: }
121: return(0);
122: }
124: int main(int argc,char **argv)
125: {
126: TS ts; /* nonlinear solver */
127: Vec x; /* solution, residual vectors */
128: Mat A; /* Jacobian matrix */
129: PetscInt steps;
130: PetscReal ftime = 0.5;
131: PetscBool monitor = PETSC_FALSE,implicitform = PETSC_TRUE;
132: PetscScalar *x_ptr;
133: PetscMPIInt size;
134: struct _n_User user;
137: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138: Initialize program
139: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
140: PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
141: MPI_Comm_size(PETSC_COMM_WORLD,&size);
142: if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");
144: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145: Set runtime options
146: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147: user.next_output = 0.0;
148: user.mu = 1.0e3;
149: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
150: PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL);
151: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
152: PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);
153: PetscOptionsEnd();
155: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: Create necessary matrix and vectors, solve same ODE on every process
157: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158: MatCreate(PETSC_COMM_WORLD,&A);
159: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
160: MatSetFromOptions(A);
161: MatSetUp(A);
163: MatCreateVecs(A,&x,NULL);
165: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
166: Create timestepping solver context
167: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
168: TSCreate(PETSC_COMM_WORLD,&ts);
169: if (implicitform) {
170: TSSetIFunction(ts,NULL,IFunction,&user);
171: TSSetIJacobian(ts,A,A,IJacobian,&user);
172: TSSetType(ts,TSBEULER);
173: } else {
174: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
175: TSSetType(ts,TSRK);
176: }
177: TSSetMaxTime(ts,ftime);
178: TSSetTimeStep(ts,0.001);
179: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
180: if (monitor) {
181: TSMonitorSet(ts,Monitor,&user,NULL);
182: }
184: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185: Set initial conditions
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
187: VecGetArray(x,&x_ptr);
188: x_ptr[0] = 2.0;
189: x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu);
190: VecRestoreArray(x,&x_ptr);
192: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
193: Set runtime options
194: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
195: TSSetFromOptions(ts);
197: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
198: Solve nonlinear system
199: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
200: TSSolve(ts,x);
201: TSGetSolveTime(ts,&ftime);
202: TSGetStepNumber(ts,&steps);
203: PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);
204: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
206: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
207: Free work space. All PETSc objects should be destroyed when they
208: are no longer needed.
209: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
210: MatDestroy(&A);
211: VecDestroy(&x);
212: TSDestroy(&ts);
214: PetscFinalize();
215: return(ierr);
216: }
218: /*TEST
220: test:
221: requires: !single
222: args: -mu 1e6
224: test:
225: requires: !single
226: suffix: 2
227: args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp
229: test:
230: requires: !single
231: suffix: 3
232: args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312
234: TEST*/