[petsc-users] Does this mean the matrix is ill-conditioned?

[Matthew Knepley]

On Wed, Jul 11, 2012 at 12:40 PM, Bao Kai <paeanball at gmail.com> wrote:

> Hi, all,
>
> The following is the output from the solution of a Poisson equation
> from Darcy's law.
>
> To compute the condition number of matrix, I did not use PC and use
> GMRES KSP to do the test.
>
> It seems like that the condition number keep increasing during the
> iterative solution. Does this mean the matrix is ill-conditioned?
>

Generally yes. Krylov methods take a long time to resolve the smallest
eigenvalues, so this approximation is not great.


> For this test, it did not achieve convergence with 10000 iterations.
>
> When I use BJOCABI PC and BICGSTAB KSP, it generally takes about 600
> times iteration to get the iteration convergent.
>
> Any suggestion for improving the convergence rate will be much
> appreciated.  The solution of this equation has been the bottleneck of
> my code, it takes more than 90% of the total time.
>

Try ML or GAMG.

    Matt


> Thank you very much.
>
> Best Regards,
> Kai
>



-- 
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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