[petsc-users] DGMRES Right preconditioner

[Gong Ding]

The order of the preconditioner is the problem.
I would like to use my own preconditioner i.e. M_D first, then the deflation preconditioner M.
That is solving 
(A*M_D^-1*M^-1) (M M_D) x = b

M_D is a static preconditioner build from A (i.e ILU or some preconditioner based on domain decomposition). And M is the deflation preconditioner build from AM_D^-1.
Anyway, since M is a dynamic preconditioner built from GMRES Arnoldi process, it is easy to be constructed from AM_D^-1.
However build preconditioner such as ILU from AM^-1 is more difficult.  

I think it is reasonable to change the order of preconditioner in DGMRES code. Or at least gives an option to do this.


> Hi Gong,
> You do not need to modify the source code for the right preconditioning.
> The additional preconditioner (say M_D^{-1}) is built from the 
> approximate eigenvalues of  M^{-1}A  or AM^{-1}.
>  Hence you are solving either M_D^{-1}M_{-1}Ax = M_D^{-1}M_{-1}b or 
> AM^{-1}M^{-1}_Dy = b for x  = M^{-1}M^{-1}_Dy
> 
> Thanks
> Desire
>