Actual source code: ex2.c
petsc-3.8.3 2017-12-09
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 =
12: */
15: /*
16: Include "petscts.h" so that we can use TS solvers. Note that this
17: file automatically includes:
18: petscsys.h - base PETSc routines petscvec.h - vectors
19: petscmat.h - matrices
20: petscis.h - index sets petscksp.h - Krylov subspace methods
21: petscviewer.h - viewers petscpc.h - preconditioners
22: petscksp.h - linear solvers
23: */
24: #include <petscts.h>
26: typedef struct {
27: PetscScalar k1,k2,k3;
28: PetscScalar sigma2;
29: Vec initialsolution;
30: } AppCtx;
32: PetscScalar k1(AppCtx *ctx,PetscReal t)
33: {
34: PetscReal th = t/3600.0;
35: PetscReal barth = th - 24.0*PetscFloorReal(th/24.0);
36: if (((((PetscInt)th) % 24) < 4) || ((((PetscInt)th) % 24) >= 20)) return(1.0e-40);
37: else return(ctx->k1*PetscExpReal(7.0*PetscPowReal(PetscSinReal(.0625*PETSC_PI*(barth - 4.0)),.2)));
38: }
40: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
41: {
42: PetscErrorCode ierr;
43: PetscScalar *f;
44: const PetscScalar *u,*udot;
47: VecGetArrayRead(U,&u);
48: VecGetArrayRead(Udot,&udot);
49: VecGetArray(F,&f);
50: f[0] = udot[0] - k1(ctx,t)*u[2] + ctx->k2*u[0];
51: f[1] = udot[1] - k1(ctx,t)*u[2] + ctx->k3*u[1]*u[3] - ctx->sigma2;
52: f[2] = udot[2] - ctx->k3*u[1]*u[3] + k1(ctx,t)*u[2];
53: f[3] = udot[3] - ctx->k2*u[0] + ctx->k3*u[1]*u[3];
54: VecRestoreArrayRead(U,&u);
55: VecRestoreArrayRead(Udot,&udot);
56: VecRestoreArray(F,&f);
57: return(0);
58: }
60: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
61: {
62: PetscErrorCode ierr;
63: PetscInt rowcol[] = {0,1,2,3};
64: PetscScalar J[4][4];
65: const PetscScalar *u,*udot;
68: VecGetArrayRead(U,&u);
69: VecGetArrayRead(Udot,&udot);
70: J[0][0] = a + ctx->k2; J[0][1] = 0.0; J[0][2] = -k1(ctx,t); J[0][3] = 0.0;
71: 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];
72: 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];
73: 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];
74: MatSetValues(B,4,rowcol,4,rowcol,&J[0][0],INSERT_VALUES);
75: VecRestoreArrayRead(U,&u);
76: VecRestoreArrayRead(Udot,&udot);
78: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
79: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
80: if (A != B) {
81: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
82: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
83: }
84: return(0);
85: }
87: static PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *ctx)
88: {
92: VecCopy(ctx->initialsolution,U);
93: if (t > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Solution not given");
94: return(0);
95: }
97: int main(int argc,char **argv)
98: {
99: TS ts; /* ODE integrator */
100: Vec U; /* solution */
101: Mat A; /* Jacobian matrix */
103: PetscMPIInt size;
104: PetscInt n = 4;
105: AppCtx ctx;
106: PetscScalar *u;
108: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109: Initialize program
110: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
112: MPI_Comm_size(PETSC_COMM_WORLD,&size);
113: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
115: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116: Create necessary matrix and vectors
117: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
118: MatCreate(PETSC_COMM_WORLD,&A);
119: MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
120: MatSetFromOptions(A);
121: MatSetUp(A);
123: MatCreateVecs(A,&U,NULL);
125: ctx.k1 = 1.0e-5;
126: ctx.k2 = 1.0e5;
127: ctx.k3 = 1.0e-16;
128: ctx.sigma2 = 1.0e6;
130: VecDuplicate(U,&ctx.initialsolution);
131: VecGetArray(ctx.initialsolution,&u);
132: u[0] = 0.0;
133: u[1] = 1.3e8;
134: u[2] = 5.0e11;
135: u[3] = 8.0e11;
136: VecRestoreArray(ctx.initialsolution,&u);
138: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139: Create timestepping solver context
140: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
141: TSCreate(PETSC_COMM_WORLD,&ts);
142: TSSetProblemType(ts,TS_NONLINEAR);
143: TSSetType(ts,TSROSW);
144: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
145: TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);
147: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: Set initial conditions
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: Solution(ts,0,U,&ctx);
151: TSSetTime(ts,4.0*3600);
152: TSSetTimeStep(ts,1.0);
153: TSSetSolution(ts,U);
155: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: Set solver options
157: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158: TSSetMaxTime(ts,518400.0);
159: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
160: TSSetMaxStepRejections(ts,100);
161: TSSetMaxSNESFailures(ts,-1); /* unlimited */
162: TSSetFromOptions(ts);
164: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165: Solve nonlinear system
166: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167: TSSolve(ts,U);
169: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
170: Free work space. All PETSc objects should be destroyed when they
171: are no longer needed.
172: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
173: VecDestroy(&ctx.initialsolution);
174: MatDestroy(&A);
175: VecDestroy(&U);
176: TSDestroy(&ts);
178: PetscFinalize();
179: return ierr;
180: }