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