hints wanted for huge eigenvalue problem

[Christian May]

Dear all,

I want to extract the lowest eigenvalues of a huge generalized 
eigenvalue problem with very dense clusters of eigenvalues.
I use slepc and superlu as external direct solver with the following 
options

-eps_ncv 300 -eps_nev 220 -eps_tol 1e-10
-st_ksp_rtol 1e-14 -st_ksp_type preonly 
-st_pc_type lu -st_pc_factor_mat_solver_package superlu_dist

Without shift-and-invert, this simply takes way too long, even on 48 CPUs 
it runs for hours.

If I use a shift-and-invert technique additionally invoking
-st_type sinvert -st_shift -0.41,

it converges very fast and also 
parallelizes well, but I most likely don't get the lowest eigenvalues if 
st_shift is slightly too high. If it's slightly too low, it doesn't seem 
to converge.

Can anybody give me some hints on how to tweak the options?
If a 100MB tar ball is not too much for you, the matrix is here:
www.phys.ethz.ch/~cmay/binaryoutput.tgz

Thanks in advance
Christian