Actual source code: ex20.c
petsc-3.13.6 2020-09-29
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: }
55: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
56: {
57: PetscErrorCode ierr;
58: User user = (User)ctx;
59: const PetscScalar *x,*xdot;
60: PetscScalar *f;
63: VecGetArrayRead(X,&x);
64: VecGetArrayRead(Xdot,&xdot);
65: VecGetArray(F,&f);
66: f[0] = xdot[0] - x[1];
67: f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]);
68: VecRestoreArrayRead(X,&x);
69: VecRestoreArrayRead(Xdot,&xdot);
70: VecRestoreArray(F,&f);
71: return(0);
72: }
74: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
75: {
76: PetscErrorCode ierr;
77: User user = (User)ctx;
78: PetscInt rowcol[] = {0,1};
79: const PetscScalar *x;
80: PetscScalar J[2][2];
83: VecGetArrayRead(X,&x);
84: J[0][0] = a; J[0][1] = -1.0;
85: 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]);
86: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
87: VecRestoreArrayRead(X,&x);
89: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
90: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
91: if (A != B) {
92: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
93: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
94: }
95: return(0);
96: }
98: /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
99: static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
100: {
101: PetscErrorCode ierr;
102: const PetscScalar *x;
103: PetscReal tfinal, dt;
104: User user = (User)ctx;
105: Vec interpolatedX;
108: TSGetTimeStep(ts,&dt);
109: TSGetMaxTime(ts,&tfinal);
111: while (user->next_output <= t && user->next_output <= tfinal) {
112: VecDuplicate(X,&interpolatedX);
113: TSInterpolate(ts,user->next_output,interpolatedX);
114: VecGetArrayRead(interpolatedX,&x);
115: PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",
116: user->next_output,step,t,dt,(double)PetscRealPart(x[0]),
117: (double)PetscRealPart(x[1]));
118: VecRestoreArrayRead(interpolatedX,&x);
119: VecDestroy(&interpolatedX);
120: user->next_output += 0.1;
121: }
122: return(0);
123: }
125: int main(int argc,char **argv)
126: {
127: TS ts; /* nonlinear solver */
128: Vec x; /* solution, residual vectors */
129: Mat A; /* Jacobian matrix */
130: PetscInt steps;
131: PetscReal ftime = 0.5;
132: PetscBool monitor = PETSC_FALSE,implicitform = PETSC_TRUE;
133: PetscScalar *x_ptr;
134: PetscMPIInt size;
135: struct _n_User user;
138: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139: Initialize program
140: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
141: PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
142: MPI_Comm_size(PETSC_COMM_WORLD,&size);
143: if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");
145: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146: Set runtime options
147: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
148: user.next_output = 0.0;
149: user.mu = 1.0e3;
150: PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);
151: PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL);
152: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
153: PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);
154: PetscOptionsEnd();
156: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: Create necessary matrix and vectors, solve same ODE on every process
158: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
159: MatCreate(PETSC_COMM_WORLD,&A);
160: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);
161: MatSetFromOptions(A);
162: MatSetUp(A);
164: MatCreateVecs(A,&x,NULL);
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Create timestepping solver context
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: TSCreate(PETSC_COMM_WORLD,&ts);
170: if (implicitform) {
171: TSSetIFunction(ts,NULL,IFunction,&user);
172: TSSetIJacobian(ts,A,A,IJacobian,&user);
173: TSSetType(ts,TSBEULER);
174: } else {
175: TSSetRHSFunction(ts,NULL,RHSFunction,&user);
176: TSSetType(ts,TSRK);
177: }
178: TSSetMaxTime(ts,ftime);
179: TSSetTimeStep(ts,0.001);
180: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
181: if (monitor) {
182: TSMonitorSet(ts,Monitor,&user,NULL);
183: }
185: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
186: Set initial conditions
187: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188: VecGetArray(x,&x_ptr);
189: x_ptr[0] = 2.0;
190: x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu);
191: VecRestoreArray(x,&x_ptr);
193: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194: Set runtime options
195: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
196: TSSetFromOptions(ts);
198: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
199: Solve nonlinear system
200: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
201: TSSolve(ts,x);
202: TSGetSolveTime(ts,&ftime);
203: TSGetStepNumber(ts,&steps);
204: PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);
205: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
207: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
208: Free work space. All PETSc objects should be destroyed when they
209: are no longer needed.
210: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
211: MatDestroy(&A);
212: VecDestroy(&x);
213: TSDestroy(&ts);
215: PetscFinalize();
216: return(ierr);
217: }
219: /*TEST
221: test:
222: requires: !single
223: args: -mu 1e6
225: test:
226: requires: !single
227: suffix: 2
228: args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp
230: test:
231: requires: !single
232: suffix: 3
233: args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312
235: TEST*/