[petsc-users] ml precondioner

[Nakib Haider Protik]

Hello

I have a 2 dimensional Poisson problem and the Laplacian is defined on a
mesh that has both uniform and non-uniform regimes. I am using the
following command:

-pc_type ml -mg_levels_ksp_type gmres -mg_levels_pc_type lu

This gives a good result. (However, if I don't specify the
-mg_level_ksp_type and -mg_levels_pc_type to gmres and lu respectively,
the default are used (richardson and sor respectively). These lead to
wrong results and the solver is extremely slow.)

Now, the following method:

-ksp_type gmres -pc_type lu

gives a slightly better result and is faster. The speed difference is
quite conspicuous for a 501 x 1001 grid size.

According to my limited knowledge, asymmetric matrices are better dealt
with by gmres and lu. However, multigrid methods are supposed to have O(n)
complexity. Why is the non-multigrid method doing better in both speed and
accuracy?

Any input would be greatly appreciated.

Thank you.

-- 
Nakib :)