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(PETSC_SUCCESS); 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(PETSC_SUCCESS); 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; 76 J[0][1] = -1.0; 77 J[1][0] = user->mu * (2.0 * x[0] * x[1] + 1.0); 78 J[1][1] = a - user->mu * (1.0 - x[0] * x[0]); 79 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 80 PetscCall(VecRestoreArrayRead(X, &x)); 81 82 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 83 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 84 if (A != B) { 85 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 86 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 87 } 88 PetscFunctionReturn(PETSC_SUCCESS); 89 } 90 91 /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */ 92 static PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal t, Vec X, void *ctx) 93 { 94 const PetscScalar *x; 95 PetscReal tfinal, dt; 96 User user = (User)ctx; 97 Vec interpolatedX; 98 99 PetscFunctionBeginUser; 100 PetscCall(TSGetTimeStep(ts, &dt)); 101 PetscCall(TSGetMaxTime(ts, &tfinal)); 102 103 while (user->next_output <= t && user->next_output <= tfinal) { 104 PetscCall(VecDuplicate(X, &interpolatedX)); 105 PetscCall(TSInterpolate(ts, user->next_output, interpolatedX)); 106 PetscCall(VecGetArrayRead(interpolatedX, &x)); 107 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "[%.1f] %" PetscInt_FMT " TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n", (double)user->next_output, step, (double)t, (double)dt, (double)PetscRealPart(x[0]), (double)PetscRealPart(x[1]))); 108 PetscCall(VecRestoreArrayRead(interpolatedX, &x)); 109 PetscCall(VecDestroy(&interpolatedX)); 110 user->next_output += 0.1; 111 } 112 PetscFunctionReturn(PETSC_SUCCESS); 113 } 114 115 int main(int argc, char **argv) 116 { 117 TS ts; /* nonlinear solver */ 118 Vec x; /* solution, residual vectors */ 119 Mat A; /* Jacobian matrix */ 120 PetscInt steps; 121 PetscReal ftime = 0.5; 122 PetscBool monitor = PETSC_FALSE, implicitform = PETSC_TRUE; 123 PetscScalar *x_ptr; 124 PetscMPIInt size; 125 struct _n_User user; 126 127 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 128 Initialize program 129 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 130 PetscFunctionBeginUser; 131 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 132 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 133 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!"); 134 135 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 136 Set runtime options 137 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 138 user.next_output = 0.0; 139 user.mu = 1.0e3; 140 PetscCall(PetscOptionsGetBool(NULL, NULL, "-monitor", &monitor, NULL)); 141 PetscCall(PetscOptionsGetBool(NULL, NULL, "-implicitform", &implicitform, NULL)); 142 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Physical parameters", NULL); 143 PetscCall(PetscOptionsReal("-mu", "Stiffness parameter", "<1.0e6>", user.mu, &user.mu, NULL)); 144 PetscOptionsEnd(); 145 146 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 147 Create necessary matrix and vectors, solve same ODE on every process 148 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 149 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 150 PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, 2, 2)); 151 PetscCall(MatSetFromOptions(A)); 152 PetscCall(MatSetUp(A)); 153 154 PetscCall(MatCreateVecs(A, &x, NULL)); 155 156 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 157 Create timestepping solver context 158 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 159 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 160 if (implicitform) { 161 PetscCall(TSSetIFunction(ts, NULL, IFunction, &user)); 162 PetscCall(TSSetIJacobian(ts, A, A, IJacobian, &user)); 163 PetscCall(TSSetType(ts, TSBEULER)); 164 } else { 165 PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &user)); 166 PetscCall(TSSetType(ts, TSRK)); 167 } 168 PetscCall(TSSetMaxTime(ts, ftime)); 169 PetscCall(TSSetTimeStep(ts, 0.001)); 170 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 171 if (monitor) PetscCall(TSMonitorSet(ts, Monitor, &user, NULL)); 172 173 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 174 Set initial conditions 175 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 176 PetscCall(VecGetArray(x, &x_ptr)); 177 x_ptr[0] = 2.0; 178 x_ptr[1] = -2.0 / 3.0 + 10.0 / (81.0 * user.mu) - 292.0 / (2187.0 * user.mu * user.mu); 179 PetscCall(VecRestoreArray(x, &x_ptr)); 180 181 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 182 Set runtime options 183 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 184 PetscCall(TSSetFromOptions(ts)); 185 186 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 187 Solve nonlinear system 188 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 189 PetscCall(TSSolve(ts, x)); 190 PetscCall(TSGetSolveTime(ts, &ftime)); 191 PetscCall(TSGetStepNumber(ts, &steps)); 192 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "steps %" PetscInt_FMT ", ftime %g\n", steps, (double)ftime)); 193 PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD)); 194 195 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 196 Free work space. All PETSc objects should be destroyed when they 197 are no longer needed. 198 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 199 PetscCall(MatDestroy(&A)); 200 PetscCall(VecDestroy(&x)); 201 PetscCall(TSDestroy(&ts)); 202 203 PetscCall(PetscFinalize()); 204 return (0); 205 } 206 207 /*TEST 208 209 test: 210 requires: !single 211 args: -mu 1e6 212 213 test: 214 requires: !single 215 suffix: 2 216 args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp 217 218 test: 219 requires: !single 220 suffix: 3 221 args: -implicitform false -ts_type rk -ts_rk_type 5dp -ts_adapt_type dsp -ts_adapt_dsp_filter H0312 222 223 TEST*/ 224