[petsc-users] AMG using ML : Advanced monitoring

[Jed Brown]

On Fri, May 11, 2012 at 3:47 PM, Karthik Duraisamy <dkarthik at stanford.edu>wrote:

> Dear all,
>
>      I have been able to use AMG (using ML) for some of my problems and am
> looking to delve deeper into the workings of the algorithm to better
> understand how to use it for larger and more complex problems. Since my
> problems are hyperbolic and involve sharp gradients, I think there is a
> possibility that coarse level operators are not very stable in some
> problems. I see evidence of this because in many cases, I need to use lu or
> a very high k ilu(k) on coarser levels to keep the iterative solver from
> diverging.
>
>    In this regard, I am wondering whether it is possible to obtain the
> coarse grid operators (or at the very least, the eigenstructure at these
> levels). Right now, I am doing the monitoring at the baseline level but I
> am looking for additional information.
>

You can estimate eigenvalues with a Krylov method using (e.g. on level 4)

-mg_levels_4_ksp_type gmres -mg_levels_4_ksp_gmres_restart 300
-mg_levels_4_ksp_gmres_max_it 300 -mg_levels_4_ksp_compute_eigenvalues
-mg_levels_4_pc_type none

(use -mg_levels_4_pc_type xxx to look at the condition number of the
preconditioned operator, use -mg_levels_4_ksp_plot_eigenvalues to make a
simple graph in an X11 window). You can also access levels from code
through the PCMG interface.

We recently got news that a proposal was funded which had a part dedicated
to interactive eigenanalysis of multilevel/hierarchical solvers. That
project will enable us to also plot specific eigenvectors and to examine
more targeted contexts (e.g. the spectrum of compatible relaxation and
other "filtered" operators).

What visualization software do you use? I am planning to support plotting
eigenvectors using VisIt and ParaView, but haven't set a relative priority
yet, so it would be useful to know what potential users care most about.

Please let me know if you have ideas for useful spectral analysis
functionality, especially with respect to understanding multigrid
convergence.
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