[petsc-users] Query regarding convergence of KSP solver

[Jed Brown]

Rachit Prasad <rachitp at vt.edu> writes:

> Hello,
>
> I am working to solve a linear system of equations using a KSP solver. The
> size of the matrix is approximately ~370,000. The following settings have
> been used to set up the solver"
>
> [image: Inline image 1]
>
> The L2 norm of the RHS for this problem is ~365, which has been calculated
> using the subroutine *VecNorm*. When I solve this system, I am finding that
> irrespective of the number of maximum iterations the L2 norm of final
> residual is pretty much constant around ~37860. 

Your solver has stagnated, either due to numerical precision issues
(e.g., if the matrix entries are enormous in this case) or (more likely)
due to an inadequate/unstable preconditioner.

> The L2 norm of the residual has been found using the subroutine
> *KSPGetResidualNorm. *The following is how the residual is varying for
> different maximum iterations.  *[image: Inline image 2]*
>
> With such being the case, I have the following doubts to clarify:
>
>    - Are the settings used by me for the KSP solver adequate enough? Or am
>    I missing something?
>    - What could be reasons for my KSP solver to not converge below the
>    permissible tolerance?
>    - For a linear system of given size, how can one determine the number of
>    maximum iterations that should be set for the KSP solver? Is there a thumb
>    rule?
>
>
> Regards,
> Rachit Prasad
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