int main(int argc,char **argv)
{
TS ts;
Vec x,c;
PetscErrorCode ierr;
DM da;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = TSCreate(PETSC_COMM_WORLD, &ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSCN);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-4,-4,PETSC_DECIDE,PETSC_DECIDE,1,1,PETSC_NULL,PETSC_NULL,&da);CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);CHKERRQ(ierr);
ierr = DMDASetFieldName(da,0,"Heat");CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = FormInitialGuess(da,PETSC_NULL,x);CHKERRQ(ierr);
ierr = DMDATSSetIFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,PetscReal,void*,void*,void*,void*))FormIFunctionLocal,PETSC_NULL);CHKERRQ(ierr);
/* set up the coefficient */
ierr = DMGetNamedGlobalVector(da,"coefficient",&c);CHKERRQ(ierr);
ierr = FormDiffusionCoefficient(da,PETSC_NULL,c);CHKERRQ(ierr);
ierr = DMRestoreNamedGlobalVector(da,"coefficient",&c);CHKERRQ(ierr);
ierr = DMCoarsenHookAdd(da,PETSC_NULL,CoefficientRestrictHook,ts);CHKERRQ(ierr);
ierr = DMSubDomainHookAdd(da,PETSC_NULL,CoefficientSubDomainRestrictHook,ts);CHKERRQ(ierr);
ierr = TSSetDM(ts, da);CHKERRQ(ierr);
ierr = TSSetDuration(ts,10000,1000.0);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,0.05);CHKERRQ(ierr);
ierr = TSSetSolution(ts,x);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
ierr = TSSolve(ts,x);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
PatternCtx user;
TS ts;
Vec x;
DMDALocalInfo info;
double noiselevel = -1.0; // negative value means no initial noise
PetscInitialize(&argc,&argv,(char*)0,help);
// parameter values from pages 21-22 in Hundsdorfer & Verwer (2003)
user.L = 2.5;
user.Du = 8.0e-5;
user.Dv = 4.0e-5;
user.phi = 0.024;
user.kappa = 0.06;
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "ptn_", "options for patterns", ""); CHKERRQ(ierr);
ierr = PetscOptionsReal("-noisy_init",
"initialize u,v with this much random noise (e.g. 0.2) on top of usual initial values",
"pattern.c",noiselevel,&noiselevel,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-L","square domain side length; recommend L >= 0.5",
"pattern.c",user.L,&user.L,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-Du","diffusion coefficient of first equation",
"pattern.c",user.Du,&user.Du,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-Dv","diffusion coefficient of second equation",
"pattern.c",user.Dv,&user.Dv,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-phi","dimensionless feed rate (=F in (Pearson, 1993))",
"pattern.c",user.phi,&user.phi,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-kappa","dimensionless rate constant (=k in (Pearson, 1993))",
"pattern.c",user.kappa,&user.kappa,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd(); CHKERRQ(ierr);
//DMDACREATE
ierr = DMDACreate2d(PETSC_COMM_WORLD,
DM_BOUNDARY_PERIODIC, DM_BOUNDARY_PERIODIC,
DMDA_STENCIL_BOX, // for 9-point stencil
4,4,PETSC_DECIDE,PETSC_DECIDE,
2, 1, // degrees of freedom, stencil width
NULL,NULL,&user.da); CHKERRQ(ierr);
//ENDDMDACREATE
ierr = DMSetFromOptions(user.da); CHKERRQ(ierr);
ierr = DMSetUp(user.da); CHKERRQ(ierr);
ierr = DMDASetFieldName(user.da,0,"u"); CHKERRQ(ierr);
ierr = DMDASetFieldName(user.da,1,"v"); CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(user.da,&info); CHKERRQ(ierr);
if (info.mx != info.my) {
SETERRQ(PETSC_COMM_WORLD,1,"pattern.c requires mx == my");
}
ierr = DMDASetUniformCoordinates(user.da, 0.0, user.L, 0.0, user.L, -1.0, -1.0); CHKERRQ(ierr);
ierr = DMSetApplicationContext(user.da,&user); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"running on %d x %d grid with square cells of side h = %.6f ...\n",
info.mx,info.my,user.L/(double)(info.mx)); CHKERRQ(ierr);
//TSSETUP
ierr = TSCreate(PETSC_COMM_WORLD,&ts); CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR); CHKERRQ(ierr);
ierr = TSSetDM(ts,user.da); CHKERRQ(ierr);
ierr = DMDATSSetRHSFunctionLocal(user.da,INSERT_VALUES,
(DMDATSRHSFunctionLocal)FormRHSFunctionLocal,&user); CHKERRQ(ierr);
ierr = DMDATSSetIFunctionLocal(user.da,INSERT_VALUES,
(DMDATSIFunctionLocal)FormIFunctionLocal,&user); CHKERRQ(ierr);
ierr = DMDATSSetIJacobianLocal(user.da,
(DMDATSIJacobianLocal)FormIJacobianLocal,&user); CHKERRQ(ierr);
ierr = TSSetType(ts,TSARKIMEX); CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP); CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,5.0); CHKERRQ(ierr); // t_0 = 0.0, dt = 5.0
ierr = TSSetDuration(ts,1000000,200.0); CHKERRQ(ierr); // t_f = 200
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
//ENDTSSETUP
ierr = DMCreateGlobalVector(user.da,&x); CHKERRQ(ierr);
ierr = InitialState(x,noiselevel,&user); CHKERRQ(ierr);
ierr = TSSolve(ts,x); CHKERRQ(ierr);
VecDestroy(&x); TSDestroy(&ts); DMDestroy(&user.da);
PetscFinalize();
return 0;
}