1 2 static char help[] = "Solves the van der Pol equation.\n\ 3 Input parameters include:\n"; 4 5 /* ------------------------------------------------------------------------ 6 7 This program solves the van der Pol DAE ODE equivalent 8 y' = z (1) 9 z' = \mu ((1-y^2)z-y) 10 on the domain 0 <= x <= 1, with the boundary conditions 11 y(0) = 2, y'(0) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2), 12 and 13 \mu = 10^6 ( y'(0) ~ -0.6666665432100101). 14 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. 15 16 Notes: 17 This code demonstrates the TS solver interface to an ODE -- RHSFunction for explicit form and IFunction for implicit form. 18 19 ------------------------------------------------------------------------- */ 20 21 #include <petscts.h> 22 23 typedef struct _n_User *User; 24 struct _n_User { 25 PetscReal mu; 26 PetscReal next_output; 27 }; 28 29 /* 30 User-defined routines 31 */ 32 static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ctx) 33 { 34 User user = (User)ctx; 35 PetscScalar *f; 36 const PetscScalar *x; 37 38 PetscFunctionBeginUser; 39 PetscCall(VecGetArrayRead(X,&x)); 40 PetscCall(VecGetArray(F,&f)); 41 f[0] = x[1]; 42 f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0]; 43 PetscCall(VecRestoreArrayRead(X,&x)); 44 PetscCall(VecRestoreArray(F,&f)); 45 PetscFunctionReturn(0); 46 } 47 48 static PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx) 49 { 50 User user = (User)ctx; 51 const PetscScalar *x,*xdot; 52 PetscScalar *f; 53 54 PetscFunctionBeginUser; 55 PetscCall(VecGetArrayRead(X,&x)); 56 PetscCall(VecGetArrayRead(Xdot,&xdot)); 57 PetscCall(VecGetArray(F,&f)); 58 f[0] = xdot[0] - x[1]; 59 f[1] = xdot[1] - user->mu*((1.0-x[0]*x[0])*x[1] - x[0]); 60 PetscCall(VecRestoreArrayRead(X,&x)); 61 PetscCall(VecRestoreArrayRead(Xdot,&xdot)); 62 PetscCall(VecRestoreArray(F,&f)); 63 PetscFunctionReturn(0); 64 } 65 66 static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx) 67 { 68 User user = (User)ctx; 69 PetscInt rowcol[] = {0,1}; 70 const PetscScalar *x; 71 PetscScalar J[2][2]; 72 73 PetscFunctionBeginUser; 74 PetscCall(VecGetArrayRead(X,&x)); 75 J[0][0] = a; J[0][1] = -1.0; 76 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]); 77 PetscCall(MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES)); 78 PetscCall(VecRestoreArrayRead(X,&x)); 79 80 PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 81 PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); 82 if (A != B) { 83 PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 84 PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 85 } 86 PetscFunctionReturn(0); 87 } 88 89 /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */ 90 static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx) 91 { 92 PetscErrorCode ierr; 93 const PetscScalar *x; 94 PetscReal tfinal, dt; 95 User user = (User)ctx; 96 Vec interpolatedX; 97 98 PetscFunctionBeginUser; 99 PetscCall(TSGetTimeStep(ts,&dt)); 100 PetscCall(TSGetMaxTime(ts,&tfinal)); 101 102 while (user->next_output <= t && user->next_output <= tfinal) { 103 PetscCall(VecDuplicate(X,&interpolatedX)); 104 PetscCall(TSInterpolate(ts,user->next_output,interpolatedX)); 105 PetscCall(VecGetArrayRead(interpolatedX,&x)); 106 ierr = PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n", 107 user->next_output,step,t,dt,(double)PetscRealPart(x[0]), 108 (double)PetscRealPart(x[1]));PetscCall(ierr); 109 PetscCall(VecRestoreArrayRead(interpolatedX,&x)); 110 PetscCall(VecDestroy(&interpolatedX)); 111 user->next_output += 0.1; 112 } 113 PetscFunctionReturn(0); 114 } 115 116 int main(int argc,char **argv) 117 { 118 TS ts; /* nonlinear solver */ 119 Vec x; /* solution, residual vectors */ 120 Mat A; /* Jacobian matrix */ 121 PetscInt steps; 122 PetscReal ftime = 0.5; 123 PetscBool monitor = PETSC_FALSE,implicitform = PETSC_TRUE; 124 PetscScalar *x_ptr; 125 PetscMPIInt size; 126 struct _n_User user; 127 PetscErrorCode ierr; 128 129 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 130 Initialize program 131 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 132 PetscCall(PetscInitialize(&argc,&argv,NULL,help)); 133 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 134 PetscCheck(size == 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!"); 135 136 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 137 Set runtime options 138 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 139 user.next_output = 0.0; 140 user.mu = 1.0e3; 141 PetscCall(PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL)); 142 PetscCall(PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL)); 143 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);PetscCall(ierr); 144 PetscCall(PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL)); 145 ierr = PetscOptionsEnd();PetscCall(ierr); 146 147 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 148 Create necessary matrix and vectors, solve same ODE on every process 149 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 150 PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); 151 PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2)); 152 PetscCall(MatSetFromOptions(A)); 153 PetscCall(MatSetUp(A)); 154 155 PetscCall(MatCreateVecs(A,&x,NULL)); 156 157 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 158 Create timestepping solver context 159 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 160 PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); 161 if (implicitform) { 162 PetscCall(TSSetIFunction(ts,NULL,IFunction,&user)); 163 PetscCall(TSSetIJacobian(ts,A,A,IJacobian,&user)); 164 PetscCall(TSSetType(ts,TSBEULER)); 165 } else { 166 PetscCall(TSSetRHSFunction(ts,NULL,RHSFunction,&user)); 167 PetscCall(TSSetType(ts,TSRK)); 168 } 169 PetscCall(TSSetMaxTime(ts,ftime)); 170 PetscCall(TSSetTimeStep(ts,0.001)); 171 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 172 if (monitor) { 173 PetscCall(TSMonitorSet(ts,Monitor,&user,NULL)); 174 } 175 176 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 177 Set initial conditions 178 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 179 PetscCall(VecGetArray(x,&x_ptr)); 180 x_ptr[0] = 2.0; 181 x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu); 182 PetscCall(VecRestoreArray(x,&x_ptr)); 183 184 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 185 Set runtime options 186 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 187 PetscCall(TSSetFromOptions(ts)); 188 189 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 190 Solve nonlinear system 191 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 192 PetscCall(TSSolve(ts,x)); 193 PetscCall(TSGetSolveTime(ts,&ftime)); 194 PetscCall(TSGetStepNumber(ts,&steps)); 195 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime)); 196 PetscCall(VecView(x,PETSC_VIEWER_STDOUT_WORLD)); 197 198 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 199 Free work space. All PETSc objects should be destroyed when they 200 are no longer needed. 201 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 202 PetscCall(MatDestroy(&A)); 203 PetscCall(VecDestroy(&x)); 204 PetscCall(TSDestroy(&ts)); 205 206 PetscCall(PetscFinalize()); 207 return(ierr); 208 } 209 210 /*TEST 211 212 test: 213 requires: !single 214 args: -mu 1e6 215 216 test: 217 requires: !single 218 suffix: 2 219 args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp 220 221 test: 222 requires: !single 223 suffix: 3 224 args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312 225 226 TEST*/ 227