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 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 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 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