Actual source code: ex2.c
petsc-3.12.1 2019-10-22
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: */
18: /*
19: Include "petscts.h" so that we can use TS solvers. Note that this
20: file automatically includes:
21: petscsys.h - base PETSc routines petscvec.h - vectors
22: petscmat.h - matrices
23: petscis.h - index sets petscksp.h - Krylov subspace methods
24: petscviewer.h - viewers petscpc.h - preconditioners
25: petscksp.h - linear solvers
26: */
28: #include <petscts.h>
30: typedef struct {
31: PetscScalar k1,k2,k3;
32: PetscScalar sigma2;
33: Vec initialsolution;
34: } AppCtx;
36: PetscScalar k1(AppCtx *ctx,PetscReal t)
37: {
38: PetscReal th = t/3600.0;
39: PetscReal barth = th - 24.0*PetscFloorReal(th/24.0);
40: if (((((PetscInt)th) % 24) < 4) || ((((PetscInt)th) % 24) >= 20)) return(1.0e-40);
41: else return(ctx->k1*PetscExpReal(7.0*PetscPowReal(PetscSinReal(.0625*PETSC_PI*(barth - 4.0)),.2)));
42: }
44: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
45: {
46: PetscErrorCode ierr;
47: PetscScalar *f;
48: const PetscScalar *u,*udot;
51: VecGetArrayRead(U,&u);
52: VecGetArrayRead(Udot,&udot);
53: VecGetArray(F,&f);
54: f[0] = udot[0] - k1(ctx,t)*u[2] + ctx->k2*u[0];
55: f[1] = udot[1] - k1(ctx,t)*u[2] + ctx->k3*u[1]*u[3] - ctx->sigma2;
56: f[2] = udot[2] - ctx->k3*u[1]*u[3] + k1(ctx,t)*u[2];
57: f[3] = udot[3] - ctx->k2*u[0] + ctx->k3*u[1]*u[3];
58: VecRestoreArrayRead(U,&u);
59: VecRestoreArrayRead(Udot,&udot);
60: VecRestoreArray(F,&f);
61: return(0);
62: }
64: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
65: {
66: PetscErrorCode ierr;
67: PetscInt rowcol[] = {0,1,2,3};
68: PetscScalar J[4][4];
69: const PetscScalar *u,*udot;
72: VecGetArrayRead(U,&u);
73: VecGetArrayRead(Udot,&udot);
74: J[0][0] = a + ctx->k2; J[0][1] = 0.0; J[0][2] = -k1(ctx,t); J[0][3] = 0.0;
75: J[1][0] = 0.0; J[1][1] = a + ctx->k3*u[3]; J[1][2] = -k1(ctx,t); J[1][3] = ctx->k3*u[1];
76: J[2][0] = 0.0; J[2][1] = -ctx->k3*u[3]; J[2][2] = a + k1(ctx,t); J[2][3] = -ctx->k3*u[1];
77: J[3][0] = -ctx->k2; J[3][1] = ctx->k3*u[3]; J[3][2] = 0.0; J[3][3] = a + ctx->k3*u[1];
78: MatSetValues(B,4,rowcol,4,rowcol,&J[0][0],INSERT_VALUES);
79: VecRestoreArrayRead(U,&u);
80: VecRestoreArrayRead(Udot,&udot);
82: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
83: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
84: if (A != B) {
85: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
86: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
87: }
88: return(0);
89: }
91: static PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *ctx)
92: {
96: VecCopy(ctx->initialsolution,U);
97: if (t > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Solution not given");
98: return(0);
99: }
101: int main(int argc,char **argv)
102: {
103: TS ts; /* ODE integrator */
104: Vec U; /* solution */
105: Mat A; /* Jacobian matrix */
107: PetscMPIInt size;
108: PetscInt n = 4;
109: AppCtx ctx;
110: PetscScalar *u;
112: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113: Initialize program
114: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
115: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
116: MPI_Comm_size(PETSC_COMM_WORLD,&size);
117: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
119: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120: Create necessary matrix and vectors
121: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
122: MatCreate(PETSC_COMM_WORLD,&A);
123: MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
124: MatSetFromOptions(A);
125: MatSetUp(A);
127: MatCreateVecs(A,&U,NULL);
129: ctx.k1 = 1.0e-5;
130: ctx.k2 = 1.0e5;
131: ctx.k3 = 1.0e-16;
132: ctx.sigma2 = 1.0e6;
134: VecDuplicate(U,&ctx.initialsolution);
135: VecGetArray(ctx.initialsolution,&u);
136: u[0] = 0.0;
137: u[1] = 1.3e8;
138: u[2] = 5.0e11;
139: u[3] = 8.0e11;
140: VecRestoreArray(ctx.initialsolution,&u);
142: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143: Create timestepping solver context
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145: TSCreate(PETSC_COMM_WORLD,&ts);
146: TSSetProblemType(ts,TS_NONLINEAR);
147: TSSetType(ts,TSROSW);
148: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
149: TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);
151: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152: Set initial conditions
153: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
154: Solution(ts,0,U,&ctx);
155: TSSetTime(ts,4.0*3600);
156: TSSetTimeStep(ts,1.0);
157: TSSetSolution(ts,U);
159: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: Set solver options
161: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
162: TSSetMaxTime(ts,518400.0);
163: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
164: TSSetMaxStepRejections(ts,100);
165: TSSetMaxSNESFailures(ts,-1); /* unlimited */
166: TSSetFromOptions(ts);
168: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
169: Solve nonlinear system
170: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
171: TSSolve(ts,U);
173: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
174: Free work space. All PETSc objects should be destroyed when they
175: are no longer needed.
176: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
177: VecDestroy(&ctx.initialsolution);
178: MatDestroy(&A);
179: VecDestroy(&U);
180: TSDestroy(&ts);
182: PetscFinalize();
183: return ierr;
184: }
187: /*TEST
189: test:
190: args: -ts_view -ts_max_time 2.e4
191: timeoutfactor: 15
192: requires: !single
194: TEST*/