[petsc-dev] Matrix-free preconditioners

[Jed Brown]

That's pretty much it.  You can probably easily apply the local part of
the operator so you can do a block Jacobi by running an iterative method
on subdomains.  Depending on the preconditioner, you might be able to
apply Neumann subdomain operators -- a research topic would be to set up
a BDDC-type method without explicit subdomain matrices.

Chris Eldred <chris.eldred at gmail.com> writes:

> Hey Petsc Dev,
>
> I had some questions about preconditioners, and I was hoping the list
> could help me out. Specifically, if I have a MatShell with the ability
> to compute the diagonal of the matrix; and a geometric multigrid
> hierarchy with appropriate operators defined; what are my
> preconditioner options?
>
> From reading the manual and the doc pages, it appears that my options are
> 1) Jacobi (and block variants)
> 2) Multigrid
> plus the ability to use Fieldsplit for block matrices. Then within
> multigrid, any iterative KSP (ie one that requires only matrix-vector
> products) can be used as a smoother, with the basic ones being
> Chebyshev and Richardson using Jacobi as a preconditioner.
>
> Is this correct? Is there anything else?
>
> Regards,
> Chris Eldred
>
> -- 
> Chris Eldred
> https://www.math.univ-paris13.fr/~eldred/
> Postdoctoral Fellow, LAGA, University of Paris 13
> PhD, Atmospheric Science, Colorado State University, 2015
> DOE Computational Science Graduate Fellow (Alumni)
> B.S. Applied Computational Physics, Carnegie Mellon University, 2009
> chris.eldred at gmail.com
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