[petsc-users] request suggestions for most appropriate eigenvalue solver

[Giacomo Mulas]

Hello. This is a slepc issue.

I have developed a code to compute anharmonic corrections to a harmonic
vibrational analysis of a molecule, including an explicit treatment of
accidental resonances.
This results in setting up a number of eigenvalue problems "around" pure 
harmonic states, which are my basis set. These eigenvalue problems are
sparse, and I only need a relatively small subset of the solutions. However,
what is unusual is _which_ eigenpairs I want: I want the eigenpairs whose
eigenvectors span a subspace which covers (within a predetermined accuracy)
the few pure harmonic states I am interested in. That is, I want enough
eigenpairs that the projection of my pure harmonic state on these
eigenvectors is "close enough" to it.

So far, I am relying on spectral slicing to obtain the eigenpairs in a
neighbourhood of the pure harmonic states I start from, increasing
neighbourhood radius until I cover the starting state adequately. However,
this results in a lot of waste: many eigenstates are accidentally close to
my target harmonic states, with little or no projection on them. I end up
computing 1-2 orders of magnitude more states than the needed ones (checked
a posteriori).

The best, for my needs, would be to be able to specify, in slepc, that my
target solutions are the ones with the highest projection on some vector
(or, better, subspace spanned by some vectors), instead of using a selection
criterion based on eigenvalues closest to a target or in an interval.  Is
there some (not too complex) way to "convince" slepc to work like this?  I
can think of providing my target vectors (one by one, or a linear
combination) as a starting point to generate the Krylov subspace, but then
how do I select eigenvectors to really be the ones I want?

Thanks in advance
Giacomo

-- 
_________________________________________________________________

Giacomo Mulas <gmulas at oa-cagliari.inaf.it>
_________________________________________________________________

OSSERVATORIO ASTRONOMICO DI CAGLIARI
Str. 54, Loc. Poggio dei Pini * 09012 Capoterra (CA)

Tel. (OAC): +39 070 71180 248     Fax : +39 070 71180 222
Tel. (UNICA): +39 070 675 4916
_________________________________________________________________

"When the storms are raging around you, stay right where you are"
                          (Freddy Mercury)
_________________________________________________________________