[petsc-users] Preconditioner question ASM vs SOR

[Matthew Knepley]

On Thu, Sep 17, 2015 at 7:07 AM, Erik Andreassen <erand at mek.dtu.dk> wrote:

> I have played a bit with preconditioners for the different levels in PCMG,
> and among others I have tried additive Schwartz (ASM), which does not seem
> to work very well – especially with no overlap. I’m curious to hear if
> anyone can explain why ASM with no overlap performs so much worse than SOR?
>

The point of a smoother is to wipe out the high frequencies in the error.
SOR does this (provably for the Laplacian), but there is no
reason ASM/ILU should do this. If this does not happen, then these parts of
the solution remain uncorrected when you go to the
coarse grid, and the convergence breaks down.

   Matt


> Thanks,
>
> Erik
>
>
>
> PS: I had a previous question about setting levels in GAMG, and my first
> impression is (in line with what Mark Adams wrote) that it is better to
> leave it to figure it out automatically. Also when using it as the coarse
> level preconditioner in a PCMG.
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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