Actual source code: ex2.c
petsc-3.7.3 2016-07-24
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*floor(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: }
42: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
43: {
44: PetscErrorCode ierr;
45: PetscScalar *f;
46: const PetscScalar *u,*udot;
49: VecGetArrayRead(U,&u);
50: VecGetArrayRead(Udot,&udot);
51: VecGetArray(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: VecRestoreArrayRead(U,&u);
57: VecRestoreArrayRead(Udot,&udot);
58: VecRestoreArray(F,&f);
59: return(0);
60: }
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: }
93: static PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *ctx)
94: {
98: VecCopy(ctx->initialsolution,U);
99: if (t > 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Solution not given");
100: return(0);
101: }
105: int main(int argc,char **argv)
106: {
107: TS ts; /* ODE integrator */
108: Vec U; /* solution */
109: Mat A; /* Jacobian matrix */
111: PetscMPIInt size;
112: PetscInt n = 4;
113: AppCtx ctx;
114: PetscScalar *u;
116: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117: Initialize program
118: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119: PetscInitialize(&argc,&argv,(char*)0,help);
120: MPI_Comm_size(PETSC_COMM_WORLD,&size);
121: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
123: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124: Create necessary matrix and vectors
125: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
126: MatCreate(PETSC_COMM_WORLD,&A);
127: MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
128: MatSetFromOptions(A);
129: MatSetUp(A);
131: MatCreateVecs(A,&U,NULL);
133: ctx.k1 = 1.0e-5;
134: ctx.k2 = 1.0e5;
135: ctx.k3 = 1.0e-16;
136: ctx.sigma2 = 1.0e6;
138: VecDuplicate(U,&ctx.initialsolution);
139: VecGetArray(ctx.initialsolution,&u);
140: u[0] = 0.0;
141: u[1] = 1.3e8;
142: u[2] = 5.0e11;
143: u[3] = 8.0e11;
144: VecRestoreArray(ctx.initialsolution,&u);
146: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: Create timestepping solver context
148: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149: TSCreate(PETSC_COMM_WORLD,&ts);
150: TSSetProblemType(ts,TS_NONLINEAR);
151: TSSetType(ts,TSROSW);
152: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
153: TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);
155: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: Set initial conditions
157: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158: Solution(ts,0,U,&ctx);
159: TSSetInitialTimeStep(ts,4.0*3600,1.0);
160: TSSetSolution(ts,U);
162: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: Set solver options
164: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
165: TSSetDuration(ts,1000000,518400.0);
166: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
167: TSSetMaxStepRejections(ts,100);
168: TSSetMaxSNESFailures(ts,-1); /* unlimited */
169: TSSetFromOptions(ts);
171: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
172: Solve nonlinear system
173: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
174: TSSolve(ts,U);
176: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: Free work space. All PETSc objects should be destroyed when they
178: are no longer needed.
179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
180: VecDestroy(&ctx.initialsolution);
181: MatDestroy(&A);
182: VecDestroy(&U);
183: TSDestroy(&ts);
185: PetscFinalize();
186: return(0);
187: }