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