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) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2), 17 and 18 \mu = 10^6 ( y'(0) ~ -0.6666665432100101). 19 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. 20 21 Notes: 22 This code demonstrates the TS solver interface to an ODE -- RHSFunction for explicit form and IFunction for implicit form. 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 User-defined routines 36 */ 37 static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx) 38 { 39 User user = (User)ctx; 40 PetscScalar *f; 41 const PetscScalar *x; 42 43 PetscFunctionBeginUser; 44 CHKERRQ(VecGetArrayRead(X,&x)); 45 CHKERRQ(VecGetArray(F,&f)); 46 f[0] = x[1]; 47 f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0]; 48 CHKERRQ(VecRestoreArrayRead(X,&x)); 49 CHKERRQ(VecRestoreArray(F,&f)); 50 PetscFunctionReturn(0); 51 } 52 53 static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx) 54 { 55 User user = (User)ctx; 56 const PetscScalar *x,*xdot; 57 PetscScalar *f; 58 59 PetscFunctionBeginUser; 60 CHKERRQ(VecGetArrayRead(X,&x)); 61 CHKERRQ(VecGetArrayRead(Xdot,&xdot)); 62 CHKERRQ(VecGetArray(F,&f)); 63 f[0] = xdot[0] - x[1]; 64 f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]); 65 CHKERRQ(VecRestoreArrayRead(X,&x)); 66 CHKERRQ(VecRestoreArrayRead(Xdot,&xdot)); 67 CHKERRQ(VecRestoreArray(F,&f)); 68 PetscFunctionReturn(0); 69 } 70 71 static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx) 72 { 73 User user = (User)ctx; 74 PetscInt rowcol[] = {0,1}; 75 const PetscScalar *x; 76 PetscScalar J[2][2]; 77 78 PetscFunctionBeginUser; 79 CHKERRQ(VecGetArrayRead(X,&x)); 80 J[0][0] = a; J[0][1] = -1.0; 81 J[1][0] = user->mu*(2.0*x[0]*x[1] + 1.0); J[1][1] = a - user->mu*(1.0-x[0]*x[0]); 82 CHKERRQ(MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES)); 83 CHKERRQ(VecRestoreArrayRead(X,&x)); 84 85 CHKERRQ(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 86 CHKERRQ(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); 87 if (A != B) { 88 CHKERRQ(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 89 CHKERRQ(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 90 } 91 PetscFunctionReturn(0); 92 } 93 94 /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */ 95 static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx) 96 { 97 PetscErrorCode ierr; 98 const PetscScalar *x; 99 PetscReal tfinal, dt; 100 User user = (User)ctx; 101 Vec interpolatedX; 102 103 PetscFunctionBeginUser; 104 CHKERRQ(TSGetTimeStep(ts,&dt)); 105 CHKERRQ(TSGetMaxTime(ts,&tfinal)); 106 107 while (user->next_output <= t && user->next_output <= tfinal) { 108 CHKERRQ(VecDuplicate(X,&interpolatedX)); 109 CHKERRQ(TSInterpolate(ts,user->next_output,interpolatedX)); 110 CHKERRQ(VecGetArrayRead(interpolatedX,&x)); 111 ierr = PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n", 112 user->next_output,step,t,dt,(double)PetscRealPart(x[0]), 113 (double)PetscRealPart(x[1]));CHKERRQ(ierr); 114 CHKERRQ(VecRestoreArrayRead(interpolatedX,&x)); 115 CHKERRQ(VecDestroy(&interpolatedX)); 116 user->next_output += 0.1; 117 } 118 PetscFunctionReturn(0); 119 } 120 121 int main(int argc,char **argv) 122 { 123 TS ts; /* nonlinear solver */ 124 Vec x; /* solution, residual vectors */ 125 Mat A; /* Jacobian matrix */ 126 PetscInt steps; 127 PetscReal ftime = 0.5; 128 PetscBool monitor = PETSC_FALSE,implicitform = PETSC_TRUE; 129 PetscScalar *x_ptr; 130 PetscMPIInt size; 131 struct _n_User user; 132 PetscErrorCode ierr; 133 134 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 135 Initialize program 136 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 137 ierr = PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr; 138 CHKERRMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 139 PetscCheck(size == 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!"); 140 141 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 142 Set runtime options 143 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 144 user.next_output = 0.0; 145 user.mu = 1.0e3; 146 CHKERRQ(PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL)); 147 CHKERRQ(PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL)); 148 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);CHKERRQ(ierr); 149 CHKERRQ(PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL)); 150 ierr = PetscOptionsEnd();CHKERRQ(ierr); 151 152 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 153 Create necessary matrix and vectors, solve same ODE on every process 154 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 155 CHKERRQ(MatCreate(PETSC_COMM_WORLD,&A)); 156 CHKERRQ(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2)); 157 CHKERRQ(MatSetFromOptions(A)); 158 CHKERRQ(MatSetUp(A)); 159 160 CHKERRQ(MatCreateVecs(A,&x,NULL)); 161 162 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 163 Create timestepping solver context 164 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 165 CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts)); 166 if (implicitform) { 167 CHKERRQ(TSSetIFunction(ts,NULL,IFunction,&user)); 168 CHKERRQ(TSSetIJacobian(ts,A,A,IJacobian,&user)); 169 CHKERRQ(TSSetType(ts,TSBEULER)); 170 } else { 171 CHKERRQ(TSSetRHSFunction(ts,NULL,RHSFunction,&user)); 172 CHKERRQ(TSSetType(ts,TSRK)); 173 } 174 CHKERRQ(TSSetMaxTime(ts,ftime)); 175 CHKERRQ(TSSetTimeStep(ts,0.001)); 176 CHKERRQ(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 177 if (monitor) { 178 CHKERRQ(TSMonitorSet(ts,Monitor,&user,NULL)); 179 } 180 181 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 182 Set initial conditions 183 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 184 CHKERRQ(VecGetArray(x,&x_ptr)); 185 x_ptr[0] = 2.0; 186 x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu); 187 CHKERRQ(VecRestoreArray(x,&x_ptr)); 188 189 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 190 Set runtime options 191 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 192 CHKERRQ(TSSetFromOptions(ts)); 193 194 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 195 Solve nonlinear system 196 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 197 CHKERRQ(TSSolve(ts,x)); 198 CHKERRQ(TSGetSolveTime(ts,&ftime)); 199 CHKERRQ(TSGetStepNumber(ts,&steps)); 200 CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime)); 201 CHKERRQ(VecView(x,PETSC_VIEWER_STDOUT_WORLD)); 202 203 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 204 Free work space. All PETSc objects should be destroyed when they 205 are no longer needed. 206 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 207 CHKERRQ(MatDestroy(&A)); 208 CHKERRQ(VecDestroy(&x)); 209 CHKERRQ(TSDestroy(&ts)); 210 211 ierr = PetscFinalize(); 212 return(ierr); 213 } 214 215 /*TEST 216 217 test: 218 requires: !single 219 args: -mu 1e6 220 221 test: 222 requires: !single 223 suffix: 2 224 args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp 225 226 test: 227 requires: !single 228 suffix: 3 229 args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312 230 231 TEST*/ 232