On Apr 5, 2012, at 10:22 AM, Abdul Hanan Sheikh wrote:
> Hi users and developers,
> Summer greetings from Delft.
>
>
> For the system Au = f, I want to apply a multilevel preconditioner with a KSP
> (say FGMRES) . The preconditioner
> reads as
>
> Prec = C + M^-1 (I - A*C) , where
>
> ? C reads coarse grid correction operator i.e. C = P*A_2h\R [ R
> restriction, A_2h coarse operator, P interpolation]
> ? M is say some sparse matrix (resembling to A)
> What makes it multilevel is I have to approximate coarse operator "A_2h" with
> few KSP iterations preconditioned by the above defined
> preconditioner "Prec" , but off course at the level 2h and hence at every
> coarse level until coarsest.
>
> I only know, it can be implemented with PCMG. I am little afraid of DMMG.
> Explanatory suggestions to customize PCMG for what is required are very
> appreciated.
C + M^-1 (I - A*C) is exactly a multiplicative Schwarz method with two
preconditioners. Or in another way to put it it is exactly a two level
multigrid so you can use PCMG in a straightforward way.
Do NOT use DMMG it is deprecated and being removed from PETSc.
To use PCMG you must provide the P and R with PCMGSetInterpolation and
PCMGSetRestriction. You would us
PCMGGetCoarseSolve(pc,&user.ksp_coarse);CHKERRQ(ierr);
ierr = KSPSetOptionsPrefix(user.ksp_coarse,"coarse_");CHKERRQ(ierr);
ierr = KSPSetFromOptions(user.ksp_coarse);CHKERRQ(ierr);
ierr =
KSPSetOperators(user.ksp_coarse,user.coarse.J,user.coarse.J,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
to provide the coarse A_c and depending what your "smoother" M is you would
possibly pass a different matrix into the second location of KSPSetOperators()
for each level to represent the "M is say some sparse matrix resembling A."
src/ksp/ksp/examples/tests/ex19.c is a simple example showing how all the
values are set for two levels.
Barry
>
> Thanks in advance.
>
>
> regards, Abdul
>
>
