1 static char help[] = "Solves the van der Pol equation.\n\
2 Input parameters include:\n";
3
4 /* ------------------------------------------------------------------------
5
6 This program solves the van der Pol DAE ODE equivalent
7 y' = z (1)
8 z' = \mu ((1-y^2)z-y)
9 on the domain 0 <= x <= 1, with the boundary conditions
10 y(0) = 2, y'(0) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2),
11 and
12 \mu = 10^6 ( y'(0) ~ -0.6666665432100101).
13 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.
14
15 Notes:
16 This code demonstrates the TS solver interface to an ODE -- RHSFunction for explicit form and IFunction for implicit form.
17
18 ------------------------------------------------------------------------- */
19
20 #include <petscts.h>
21
22 typedef struct _n_User *User;
23 struct _n_User {
24 PetscReal mu;
25 PetscReal next_output;
26 };
27
28 /*
29 User-defined routines
30 */
RHSFunction(TS ts,PetscReal t,Vec X,Vec F,PetscCtx ctx)31 static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec X, Vec F, PetscCtx ctx)
32 {
33 User user = (User)ctx;
34 PetscScalar *f;
35 const PetscScalar *x;
36
37 PetscFunctionBeginUser;
38 PetscCall(VecGetArrayRead(X, &x));
39 PetscCall(VecGetArray(F, &f));
40 f[0] = x[1];
41 f[1] = user->mu * (1. - x[0] * x[0]) * x[1] - x[0];
42 PetscCall(VecRestoreArrayRead(X, &x));
43 PetscCall(VecRestoreArray(F, &f));
44 PetscFunctionReturn(PETSC_SUCCESS);
45 }
46
IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,PetscCtx ctx)47 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, PetscCtx ctx)
48 {
49 User user = (User)ctx;
50 const PetscScalar *x, *xdot;
51 PetscScalar *f;
52
53 PetscFunctionBeginUser;
54 PetscCall(VecGetArrayRead(X, &x));
55 PetscCall(VecGetArrayRead(Xdot, &xdot));
56 PetscCall(VecGetArray(F, &f));
57 f[0] = xdot[0] - x[1];
58 f[1] = xdot[1] - user->mu * ((1.0 - x[0] * x[0]) * x[1] - x[0]);
59 PetscCall(VecRestoreArrayRead(X, &x));
60 PetscCall(VecRestoreArrayRead(Xdot, &xdot));
61 PetscCall(VecRestoreArray(F, &f));
62 PetscFunctionReturn(PETSC_SUCCESS);
63 }
64
IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,PetscCtx ctx)65 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat A, Mat B, PetscCtx ctx)
66 {
67 User user = (User)ctx;
68 PetscInt rowcol[] = {0, 1};
69 const PetscScalar *x;
70 PetscScalar J[2][2];
71
72 PetscFunctionBeginUser;
73 PetscCall(VecGetArrayRead(X, &x));
74 J[0][0] = a;
75 J[0][1] = -1.0;
76 J[1][0] = user->mu * (2.0 * x[0] * x[1] + 1.0);
77 J[1][1] = a - user->mu * (1.0 - x[0] * x[0]);
78 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES));
79 PetscCall(VecRestoreArrayRead(X, &x));
80
81 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
82 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
83 if (A != B) {
84 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
85 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
86 }
87 PetscFunctionReturn(PETSC_SUCCESS);
88 }
89
90 /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */
Monitor(TS ts,PetscInt step,PetscReal t,Vec X,PetscCtx ctx)91 static PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal t, Vec X, PetscCtx ctx)
92 {
93 const PetscScalar *x;
94 PetscReal tfinal, dt;
95 User user = (User)ctx;
96 Vec interpolatedX;
97
98 PetscFunctionBeginUser;
99 PetscCall(TSGetTimeStep(ts, &dt));
100 PetscCall(TSGetMaxTime(ts, &tfinal));
101
102 while (user->next_output <= t && user->next_output <= tfinal) {
103 PetscCall(VecDuplicate(X, &interpolatedX));
104 PetscCall(TSInterpolate(ts, user->next_output, interpolatedX));
105 PetscCall(VecGetArrayRead(interpolatedX, &x));
106 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[%.1f] %" PetscInt_FMT " TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n", (double)user->next_output, step, (double)t, (double)dt, (double)PetscRealPart(x[0]), (double)PetscRealPart(x[1])));
107 PetscCall(VecRestoreArrayRead(interpolatedX, &x));
108 PetscCall(VecDestroy(&interpolatedX));
109 user->next_output += 0.1;
110 }
111 PetscFunctionReturn(PETSC_SUCCESS);
112 }
113
main(int argc,char ** argv)114 int main(int argc, char **argv)
115 {
116 TS ts; /* nonlinear solver */
117 Vec x; /* solution, residual vectors */
118 Mat A; /* Jacobian matrix */
119 PetscInt steps;
120 PetscReal ftime = 0.5;
121 PetscBool monitor = PETSC_FALSE, implicitform = PETSC_TRUE;
122 PetscScalar *x_ptr;
123 PetscMPIInt size;
124 struct _n_User user;
125
126 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127 Initialize program
128 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
129 PetscFunctionBeginUser;
130 PetscCall(PetscInitialize(&argc, &argv, NULL, help));
131 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
132 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
133
134 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135 Set runtime options
136 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137 user.next_output = 0.0;
138 user.mu = 1.0e3;
139 PetscCall(PetscOptionsGetBool(NULL, NULL, "-monitor", &monitor, NULL));
140 PetscCall(PetscOptionsGetBool(NULL, NULL, "-implicitform", &implicitform, NULL));
141 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Physical parameters", NULL);
142 PetscCall(PetscOptionsReal("-mu", "Stiffness parameter", "<1.0e6>", user.mu, &user.mu, NULL));
143 PetscOptionsEnd();
144
145 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146 Create necessary matrix and vectors, solve same ODE on every process
147 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
148 PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
149 PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, 2, 2));
150 PetscCall(MatSetFromOptions(A));
151 PetscCall(MatSetUp(A));
152
153 PetscCall(MatCreateVecs(A, &x, NULL));
154
155 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156 Create timestepping solver context
157 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
159 if (implicitform) {
160 PetscCall(TSSetIFunction(ts, NULL, IFunction, &user));
161 PetscCall(TSSetIJacobian(ts, A, A, IJacobian, &user));
162 PetscCall(TSSetType(ts, TSBEULER));
163 } else {
164 PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &user));
165 PetscCall(TSSetType(ts, TSRK));
166 }
167 PetscCall(TSSetMaxTime(ts, ftime));
168 PetscCall(TSSetTimeStep(ts, 0.001));
169 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
170 if (monitor) PetscCall(TSMonitorSet(ts, Monitor, &user, NULL));
171
172 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
173 Set initial conditions
174 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
175 PetscCall(VecGetArray(x, &x_ptr));
176 x_ptr[0] = 2.0;
177 x_ptr[1] = -2.0 / 3.0 + 10.0 / (81.0 * user.mu) - 292.0 / (2187.0 * user.mu * user.mu);
178 PetscCall(VecRestoreArray(x, &x_ptr));
179
180 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181 Set runtime options
182 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183 PetscCall(TSSetFromOptions(ts));
184
185 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
186 Solve nonlinear system
187 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188 PetscCall(TSSolve(ts, x));
189 PetscCall(TSGetSolveTime(ts, &ftime));
190 PetscCall(TSGetStepNumber(ts, &steps));
191 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "steps %" PetscInt_FMT ", ftime %g\n", steps, (double)ftime));
192 PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD));
193
194 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195 Free work space. All PETSc objects should be destroyed when they
196 are no longer needed.
197 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198 PetscCall(MatDestroy(&A));
199 PetscCall(VecDestroy(&x));
200 PetscCall(TSDestroy(&ts));
201
202 PetscCall(PetscFinalize());
203 return 0;
204 }
205
206 /*TEST
207
208 test:
209 requires: !single
210 args: -mu 1e6
211
212 test:
213 requires: !single
214 suffix: 2
215 args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp
216
217 test:
218 requires: !single
219 suffix: 3
220 args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312
221
222 TEST*/
223