Actual source code: ex2.c
2: static char help[] = "Reaction Equation from Chemistry\n";
4: /*
6: Page 6, An example from Atomospheric Chemistry
8: u_1_t =
9: u_2_t =
10: u_3_t =
11: u_4_t =
13: -ts_monitor_lg_error -ts_monitor_lg_solution -ts_view -ts_max_time 2.e4
15: */
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: */
27: #include <petscts.h>
29: typedef struct {
30: PetscScalar k1, k2, k3;
31: PetscScalar sigma2;
32: Vec initialsolution;
33: } AppCtx;
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: }
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;
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: }
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;
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));
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: }
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: }
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;
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");
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));
134: PetscCall(MatCreateVecs(A, &U, NULL));
136: ctx.k1 = 1.0e-5;
137: ctx.k2 = 1.0e5;
138: ctx.k3 = 1.0e-16;
139: ctx.sigma2 = 1.0e6;
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));
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));
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));
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));
175: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176: Solve nonlinear system
177: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
178: PetscCall(TSSolve(ts, U));
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));
189: PetscCall(PetscFinalize());
190: return 0;
191: }
193: /*TEST
195: test:
196: args: -ts_view -ts_max_time 2.e4
197: timeoutfactor: 15
198: requires: !single
200: TEST*/