1
2 static char help[] = "Solves the van der Pol equation.\n\
3 Input parameters include:\n";
4
5 /*
6 Concepts: TS^time-dependent nonlinear problems
7 Concepts: TS^van der Pol equation DAE equivalent
8 Processors: 1
9 */
10 /* ------------------------------------------------------------------------
11
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) = -6.6e-01,
17 and
18 mu = 10^6.
19 This is a nonlinear equation.
20
21 This is a copy and modification of ex20.c to exactly match a test
22 problem that comes with the Radau5 integrator package.
23
24 ------------------------------------------------------------------------- */
25
26 #include <petscts.h>
27
28 typedef struct _n_User *User;
29 struct _n_User {
30 PetscReal mu;
31 PetscReal next_output;
32 };
33
34
IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void * ctx)35 static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
36 {
37 PetscErrorCode ierr;
38 User user = (User)ctx;
39 const PetscScalar *x,*xdot;
40 PetscScalar *f;
41
42 PetscFunctionBeginUser;
43 ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
44 ierr = VecGetArrayRead(Xdot,&xdot);CHKERRQ(ierr);
45 ierr = VecGetArray(F,&f);CHKERRQ(ierr);
46 f[0] = xdot[0] - x[1];
47 f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]);
48 ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
49 ierr = VecRestoreArrayRead(Xdot,&xdot);CHKERRQ(ierr);
50 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
51 PetscFunctionReturn(0);
52 }
53
IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void * ctx)54 static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
55 {
56 PetscErrorCode ierr;
57 User user = (User)ctx;
58 PetscInt rowcol[] = {0,1};
59 const PetscScalar *x;
60 PetscScalar J[2][2];
61
62 PetscFunctionBeginUser;
63 ierr = VecGetArrayRead(X,&x);CHKERRQ(ierr);
64 J[0][0] = a; J[0][1] = -1.0;
65 J[1][0] = user->mu*(1.0 + 2.0*x[0]*x[1]); J[1][1] = a - user->mu*(1.0-x[0]*x[0]);
66 ierr = MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr);
67 ierr = VecRestoreArrayRead(X,&x);CHKERRQ(ierr);
68
69 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
70 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
71 if (A != B) {
72 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
73 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
74 }
75 PetscFunctionReturn(0);
76 }
77
78
main(int argc,char ** argv)79 int main(int argc,char **argv)
80 {
81 TS ts; /* nonlinear solver */
82 Vec x; /* solution, residual vectors */
83 Mat A; /* Jacobian matrix */
84 PetscInt steps;
85 PetscReal ftime = 2;
86 PetscScalar *x_ptr;
87 PetscMPIInt size;
88 struct _n_User user;
89 PetscErrorCode ierr;
90
91 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92 Initialize program
93 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94 ierr = PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
95 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
96 if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");
97
98 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
99 Set runtime options
100 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101 user.next_output = 0.0;
102 user.mu = 1.0e6;
103 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
104 ierr = PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);CHKERRQ(ierr);
105 ierr = PetscOptionsEnd();CHKERRQ(ierr);
106
107 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
108 Create necessary matrix and vectors, solve same ODE on every process
109 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
110 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
111 ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);CHKERRQ(ierr);
112 ierr = MatSetFromOptions(A);CHKERRQ(ierr);
113 ierr = MatSetUp(A);CHKERRQ(ierr);
114
115 ierr = MatCreateVecs(A,&x,NULL);CHKERRQ(ierr);
116
117 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
118 Create timestepping solver context
119 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
120 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
121 ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
122 ierr = TSSetIFunction(ts,NULL,IFunction,&user);CHKERRQ(ierr);
123 ierr = TSSetIJacobian(ts,A,A,IJacobian,&user);CHKERRQ(ierr);
124
125 ierr = TSSetMaxTime(ts,ftime);CHKERRQ(ierr);
126 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
127 ierr = TSSetTolerances(ts,1.e-4,NULL,1.e-4,NULL);CHKERRQ(ierr);
128 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129 Set initial conditions
130 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131 ierr = VecGetArray(x,&x_ptr);CHKERRQ(ierr);
132 x_ptr[0] = 2.0; x_ptr[1] = -6.6e-01;
133 ierr = VecRestoreArray(x,&x_ptr);CHKERRQ(ierr);
134 ierr = TSSetTimeStep(ts,.000001);CHKERRQ(ierr);
135
136 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137 Set runtime options
138 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
139 ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
140
141 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142 Solve nonlinear system
143 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144 ierr = TSSolve(ts,x);CHKERRQ(ierr);
145 ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
146 ierr = TSGetStepNumber(ts,&steps);CHKERRQ(ierr);
147 ierr = PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);CHKERRQ(ierr);
148 ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
149
150 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151 Free work space. All PETSc objects should be destroyed when they
152 are no longer needed.
153 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
154 ierr = MatDestroy(&A);CHKERRQ(ierr);
155 ierr = VecDestroy(&x);CHKERRQ(ierr);
156 ierr = TSDestroy(&ts);CHKERRQ(ierr);
157
158 ierr = PetscFinalize();
159 return(ierr);
160 }
161
162 /*TEST
163
164 build:
165 requires: double !complex !define(PETSC_USE_64BIT_INDICES) radau5
166
167 test:
168 args: -ts_monitor_solution -ts_type radau5
169
170 TEST*/
171