1 2 static char help[] = "Reaction Equation from Chemistry\n"; 3 4 /* 5 6 Page 6, An example from Atomospheric Chemistry 7 8 u_1_t = 9 u_2_t = 10 u_3_t = 11 u_4_t = 12 13 -ts_monitor_lg_error -ts_monitor_lg_solution -ts_view -ts_max_time 2.e4 14 15 */ 16 17 /* 18 Include "petscts.h" so that we can use TS solvers. Note that this 19 file automatically includes: 20 petscsys.h - base PETSc routines petscvec.h - vectors 21 petscmat.h - matrices 22 petscis.h - index sets petscksp.h - Krylov subspace methods 23 petscviewer.h - viewers petscpc.h - preconditioners 24 petscksp.h - linear solvers 25 */ 26 27 #include <petscts.h> 28 29 typedef struct { 30 PetscScalar k1, k2, k3; 31 PetscScalar sigma2; 32 Vec initialsolution; 33 } AppCtx; 34 35 PetscScalar k1(AppCtx *ctx, PetscReal t) 36 { 37 PetscReal th = t / 3600.0; 38 PetscReal barth = th - 24.0 * PetscFloorReal(th / 24.0); 39 if (((((PetscInt)th) % 24) < 4) || ((((PetscInt)th) % 24) >= 20)) return (1.0e-40); 40 else return (ctx->k1 * PetscExpReal(7.0 * PetscPowReal(PetscSinReal(.0625 * PETSC_PI * (barth - 4.0)), .2))); 41 } 42 43 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx) 44 { 45 PetscScalar *f; 46 const PetscScalar *u, *udot; 47 48 PetscFunctionBegin; 49 PetscCall(VecGetArrayRead(U, &u)); 50 PetscCall(VecGetArrayRead(Udot, &udot)); 51 PetscCall(VecGetArrayWrite(F, &f)); 52 f[0] = udot[0] - k1(ctx, t) * u[2] + ctx->k2 * u[0]; 53 f[1] = udot[1] - k1(ctx, t) * u[2] + ctx->k3 * u[1] * u[3] - ctx->sigma2; 54 f[2] = udot[2] - ctx->k3 * u[1] * u[3] + k1(ctx, t) * u[2]; 55 f[3] = udot[3] - ctx->k2 * u[0] + ctx->k3 * u[1] * u[3]; 56 PetscCall(VecRestoreArrayRead(U, &u)); 57 PetscCall(VecRestoreArrayRead(Udot, &udot)); 58 PetscCall(VecRestoreArrayWrite(F, &f)); 59 PetscFunctionReturn(PETSC_SUCCESS); 60 } 61 62 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx) 63 { 64 PetscInt rowcol[] = {0, 1, 2, 3}; 65 PetscScalar J[4][4]; 66 const PetscScalar *u, *udot; 67 68 PetscFunctionBegin; 69 PetscCall(VecGetArrayRead(U, &u)); 70 PetscCall(VecGetArrayRead(Udot, &udot)); 71 J[0][0] = a + ctx->k2; 72 J[0][1] = 0.0; 73 J[0][2] = -k1(ctx, t); 74 J[0][3] = 0.0; 75 J[1][0] = 0.0; 76 J[1][1] = a + ctx->k3 * u[3]; 77 J[1][2] = -k1(ctx, t); 78 J[1][3] = ctx->k3 * u[1]; 79 J[2][0] = 0.0; 80 J[2][1] = -ctx->k3 * u[3]; 81 J[2][2] = a + k1(ctx, t); 82 J[2][3] = -ctx->k3 * u[1]; 83 J[3][0] = -ctx->k2; 84 J[3][1] = ctx->k3 * u[3]; 85 J[3][2] = 0.0; 86 J[3][3] = a + ctx->k3 * u[1]; 87 PetscCall(MatSetValues(B, 4, rowcol, 4, rowcol, &J[0][0], INSERT_VALUES)); 88 PetscCall(VecRestoreArrayRead(U, &u)); 89 PetscCall(VecRestoreArrayRead(Udot, &udot)); 90 91 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 92 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 93 if (A != B) { 94 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 95 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 96 } 97 PetscFunctionReturn(PETSC_SUCCESS); 98 } 99 100 static PetscErrorCode Solution(TS ts, PetscReal t, Vec U, AppCtx *ctx) 101 { 102 PetscFunctionBegin; 103 PetscCall(VecCopy(ctx->initialsolution, U)); 104 PetscCheck(t <= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Solution not given"); 105 PetscFunctionReturn(PETSC_SUCCESS); 106 } 107 108 int main(int argc, char **argv) 109 { 110 TS ts; /* ODE integrator */ 111 Vec U; /* solution */ 112 Mat A; /* Jacobian matrix */ 113 PetscMPIInt size; 114 PetscInt n = 4; 115 AppCtx ctx; 116 PetscScalar *u; 117 118 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 119 Initialize program 120 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 121 PetscFunctionBeginUser; 122 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 123 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 124 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 125 126 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 127 Create necessary matrix and vectors 128 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 129 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 130 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 131 PetscCall(MatSetFromOptions(A)); 132 PetscCall(MatSetUp(A)); 133 134 PetscCall(MatCreateVecs(A, &U, NULL)); 135 136 ctx.k1 = 1.0e-5; 137 ctx.k2 = 1.0e5; 138 ctx.k3 = 1.0e-16; 139 ctx.sigma2 = 1.0e6; 140 141 PetscCall(VecDuplicate(U, &ctx.initialsolution)); 142 PetscCall(VecGetArrayWrite(ctx.initialsolution, &u)); 143 u[0] = 0.0; 144 u[1] = 1.3e8; 145 u[2] = 5.0e11; 146 u[3] = 8.0e11; 147 PetscCall(VecRestoreArrayWrite(ctx.initialsolution, &u)); 148 149 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 150 Create timestepping solver context 151 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 152 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 153 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 154 PetscCall(TSSetType(ts, TSROSW)); 155 PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &ctx)); 156 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &ctx)); 157 158 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 159 Set initial conditions 160 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 161 PetscCall(Solution(ts, 0, U, &ctx)); 162 PetscCall(TSSetTime(ts, 4.0 * 3600)); 163 PetscCall(TSSetTimeStep(ts, 1.0)); 164 PetscCall(TSSetSolution(ts, U)); 165 166 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 167 Set solver options 168 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 169 PetscCall(TSSetMaxTime(ts, 518400.0)); 170 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 171 PetscCall(TSSetMaxStepRejections(ts, 100)); 172 PetscCall(TSSetMaxSNESFailures(ts, -1)); /* unlimited */ 173 PetscCall(TSSetFromOptions(ts)); 174 175 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 176 Solve nonlinear system 177 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 178 PetscCall(TSSolve(ts, U)); 179 180 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 181 Free work space. All PETSc objects should be destroyed when they 182 are no longer needed. 183 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 184 PetscCall(VecDestroy(&ctx.initialsolution)); 185 PetscCall(MatDestroy(&A)); 186 PetscCall(VecDestroy(&U)); 187 PetscCall(TSDestroy(&ts)); 188 189 PetscCall(PetscFinalize()); 190 return 0; 191 } 192 193 /*TEST 194 195 test: 196 args: -ts_view -ts_max_time 2.e4 197 timeoutfactor: 15 198 requires: !single 199 200 TEST*/ 201