[Trilinos-Users] AztecOO Convergence

[Ammar T. Al-Sayegh]

Randal,

Thank you for the elaborate explanation. Your reasoning makes
sense, and I tried to follow your advice and disable the
preconditioner. However, I got hit by another issue. Now it
says that my GMRES Hessenberg matrix is ill-conditioned,
which perhaps is right because I'm dealing with nonlinear
analysis of a structure that's reaching instability, i.e.
having it's stiffness matrix getting close to being singular.
The thing that I can't make sense of, though, is that why
it works fine just fine with a single processor but not
with two processors even when preconditioner is disabled?

I don't mind the additional time cost if there is a way to
get the same level of numerical accuracy of when using
multiple processors as in the case with a single processor.


-ammar


----- Original Message ----- 
From: "Randall Bramley" <bramley at cs.indiana.edu>
To: "Ammar T. Al-Sayegh" <alsayegh at purdue.edu>
Cc: <trilinos-users at software.sandia.gov>
Sent: Monday, November 21, 2005 11:01 AM
Subject: Re: [Trilinos-Users] AztecOO Convergence


> 
>> In AztecOO, why does convergence deteriorate as the number
>> of processors is increased?
> 
> At last, a question I can answer. :-)
> 
> The preprocessing is usually block diagonal, and as the number of
> processors increases, the blocks become smaller - in the limit, the
> preconditioner becomes diagonal scaling.  Fewer processors leads to
> the block becoming larger, in the limit becoming an incomplete
> factorization on the whole matrix.  This is generally a more
> accurate preconditioner since it brings in more off-diagonal elements
> and hence accounts for longer-range interactions in the linear system.
> 
> So it's normal to have the quality of preconditioning lower (and hence
> number of iterations higher) when the number of processors increases.
> 
>> Is there any options one can use to eliminate this problem?
>>
>> Are there any particular solvers which will yield same
>> convergence regardless of the number of processors?
> 
> Yes, but they are not good ones to choose: use no preconditioning or
> just diagonal scaling.  But you're likely to find the wall clock
> time increases over letting the number of iterations increase.
> 
> -Randall Bramley
>