Actual source code: ex3.c
1: static char help[] = "Basic problem for multi-rate method.\n";
\begin{eqnarray}
ys' = -2.0*\frac{-1.0+ys^2.0-\cos(t)}{2.0*ys}+0.05*\frac{-2.0+yf^2-\cos(5.0*t)}{2.0*yf}-\frac{\sin(t)}{2.0*ys}\\
yf' = 0.05*\frac{-1.0+ys^2-\cos(t)}{2.0*ys}-\frac{-2.0+yf^2-\cos(5.0*t)}{2.0*yf}-5.0*\frac{\sin(5.0*t)}{2.0*yf}\\
\end{eqnarray}
12: #include <petscts.h>
14: typedef struct {
15: PetscReal Tf,dt;
16: } AppCtx;
18: static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
19: {
20: const PetscScalar *u;
21: PetscScalar *f;
23: VecGetArrayRead(U,&u);
24: VecGetArray(F,&f);
25: f[0] = -2.0*(-1.0+u[0]*u[0]-PetscCosScalar(t))/(2.0*u[0])+0.05*(-2.0+u[1]*u[1]-PetscCosScalar(5.0*t))/(2.0*u[1])-PetscSinScalar(t)/(2.0*u[0]);
26: f[1] = 0.05*(-1.0+u[0]*u[0]-PetscCosScalar(t))/(2.0*u[0])-(-2.0+u[1]*u[1]-PetscCosScalar(5.0*t))/(2.0*u[1])-5.0*PetscSinScalar(5.0*t)/(2.0*u[1]);
27: VecRestoreArrayRead(U,&u);
28: VecRestoreArray(F,&f);
29: return 0;
30: }
32: static PetscErrorCode RHSFunctionslow(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
33: {
34: const PetscScalar *u;
35: PetscScalar *f;
37: VecGetArrayRead(U,&u);
38: VecGetArray(F,&f);
39: f[0] = -2.0*(-1.0+u[0]*u[0]-PetscCosScalar(t))/(2.0*u[0])+0.05*(-2.0+u[1]*u[1]-PetscCosScalar(5.0*t))/(2.0*u[1])-PetscSinScalar(t)/(2.0*u[0]);
40: VecRestoreArrayRead(U,&u);
41: VecRestoreArray(F,&f);
42: return 0;
43: }
45: static PetscErrorCode RHSFunctionfast(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
46: {
47: const PetscScalar *u;
48: PetscScalar *f;
50: VecGetArrayRead(U,&u);
51: VecGetArray(F,&f);
52: f[0] = 0.05*(-1.0+u[0]*u[0]-PetscCosScalar(t))/(2.0*u[0])-(-2.0+u[1]*u[1]-PetscCosScalar(5.0*t))/(2.0*u[1])-5.0*PetscSinScalar(5.0*t)/(2.0*u[1]);
53: VecRestoreArrayRead(U,&u);
54: VecRestoreArray(F,&f);
55: return 0;
56: }
58: static PetscErrorCode sol_true(PetscReal t,Vec U)
59: {
60: PetscScalar *u;
62: VecGetArray(U,&u);
63: u[0] = PetscSqrtScalar(1.0+PetscCosScalar(t));
64: u[1] = PetscSqrtScalar(2.0+PetscCosScalar(5.0*t));
65: VecRestoreArray(U,&u);
66: return 0;
67: }
69: int main(int argc,char **argv)
70: {
71: TS ts; /* ODE integrator */
72: Vec U; /* solution will be stored here */
73: Vec Utrue;
75: PetscMPIInt size;
76: AppCtx ctx;
77: PetscScalar *u;
78: IS iss;
79: IS isf;
80: PetscInt *indicess;
81: PetscInt *indicesf;
82: PetscInt n=2;
83: PetscReal error,tt;
85: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
86: Initialize program
87: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
88: PetscInitialize(&argc,&argv,(char*)0,help);
89: MPI_Comm_size(PETSC_COMM_WORLD,&size);
92: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
93: Create index for slow part and fast part
94: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
95: PetscMalloc1(1,&indicess);
96: indicess[0]=0;
97: PetscMalloc1(1,&indicesf);
98: indicesf[0]=1;
99: ISCreateGeneral(PETSC_COMM_SELF,1,indicess,PETSC_COPY_VALUES,&iss);
100: ISCreateGeneral(PETSC_COMM_SELF,1,indicesf,PETSC_COPY_VALUES,&isf);
102: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103: Create necessary vector
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105: VecCreate(PETSC_COMM_WORLD,&U);
106: VecSetSizes(U,n,PETSC_DETERMINE);
107: VecSetFromOptions(U);
108: VecDuplicate(U,&Utrue);
109: VecCopy(U,Utrue);
111: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
112: Set initial condition
113: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
114: VecGetArray(U,&u);
115: u[0] = PetscSqrtScalar(2.0);
116: u[1] = PetscSqrtScalar(3.0);
117: VecRestoreArray(U,&u);
119: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
120: Create timestepping solver context
121: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
122: TSCreate(PETSC_COMM_WORLD,&ts);
123: TSSetType(ts,TSMPRK);
125: TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
126: TSRHSSplitSetIS(ts,"slow",iss);
127: TSRHSSplitSetIS(ts,"fast",isf);
128: TSRHSSplitSetRHSFunction(ts,"slow",NULL,(TSRHSFunction)RHSFunctionslow,&ctx);
129: TSRHSSplitSetRHSFunction(ts,"fast",NULL,(TSRHSFunction)RHSFunctionfast,&ctx);
131: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132: Set initial conditions
133: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
134: TSSetSolution(ts,U);
136: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: Set solver options
138: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
139: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ODE options","");
140: {
141: ctx.Tf = 0.3;
142: ctx.dt = 0.01;
143: PetscOptionsScalar("-Tf","","",ctx.Tf,&ctx.Tf,NULL);
144: PetscOptionsScalar("-dt","","",ctx.dt,&ctx.dt,NULL);
145: }
146: PetscOptionsEnd();
147: TSSetMaxTime(ts,ctx.Tf);
148: TSSetTimeStep(ts,ctx.dt);
149: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
150: TSSetFromOptions(ts);
152: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: Solve linear system
154: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155: TSSolve(ts,U);
156: VecView(U,PETSC_VIEWER_STDOUT_WORLD);
158: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
159: Check the error of the Petsc solution
160: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
161: TSGetTime(ts,&tt);
162: sol_true(tt,Utrue);
163: VecAXPY(Utrue,-1.0,U);
164: VecNorm(Utrue,NORM_2,&error);
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Print norm2 error
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: PetscPrintf(PETSC_COMM_WORLD,"l2 error norm: %g\n", error);
171: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
172: Free work space. All PETSc objects should be destroyed when they are no longer needed.
173: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
174: VecDestroy(&U);
175: TSDestroy(&ts);
176: VecDestroy(&Utrue);
177: ISDestroy(&iss);
178: ISDestroy(&isf);
179: PetscFree(indicess);
180: PetscFree(indicesf);
181: PetscFinalize();
182: return 0;
183: }
185: /*TEST
186: build:
187: requires: !complex
189: test:
191: TEST*/