[petsc-users] BiCGSTAB for general use

[Paul Anton Letnes]

> Let's start with a scatter plot of the eigenvalues. Can you do a problem that is representative of the physics in less than, say, 1000 degrees of freedom? If so, I would just use Matlab (or Octave, etc).  You want to be able to plot the eigenvector associated with a chosen eigenvalue in some way that is meaningful to you. We want to see if the wavelength (in terms of the variables you are discretizing over) of the modes has some useful correlation with the size of the associated eigenvalues. If so, we may be able to build some sort of multigrid preconditioner.

1000 degrees of freedom is a bit little. I took a 4608 x 4608 matrix and plotted its eigenvalues as a scatterplot in the complex plane, as well as the magnitude of the eigenvalues. See attachments. I can give out better quality plots off-list.

I'm really not sure as to how one can visualize eigenvectors with 4608 elements...

I have not thought too much about the physical meaning of eigenvectors and eigenvalues. In fact, even this system is too small to be of physical interest, so I'm not sure what I'd get out of it, to be honest. I suppose some eigenvectors might be related to surface plasmon polaritons, and one eigenvector is probably related to the specular ("mirror-like") peak.

Hope this is of any relevance.
Paul
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