AW: [Libmesh-users] Eigenvalue problem

[Steffen P. <ste...@tu...>]

> Hi, I also use the generalized eigenvalue problem and it=20
> works fine. Many
> thanks. I have a question: I have a real symmetric problem,=20
> so I get only real
> eigenvalues, but I need to get the lowest ones. So I use:
>=20
> eigen_system.eigen_solver->set_position_of_spectrum(SMALLEST_M
AGNITUDE);
>=20
> The problem is, that all the solvers from slepc package=20
> (ARNOLDI, SUBSPACE,
> POWER) don't support the "SMALLEST_MAGNITUDE" option, see=20
> their sources, for
> example slepc-2.3.0/src/eps/impls/arnoldi/arnoldi.c, line 38:
>=20
>   if (eps->which!=3DEPS_LARGEST_MAGNITUDE)
>       SETERRQ(1,"Wrong value of eps->which");
>=20
> Except the "LAPACK" solver.  Lapack works fine, but it=20
> retrieves all the
> eigenvalues and is really slow, in fact for a bigger mesh=20
> it's completely
> unusable (but works). Is there a way how to get the lowest=20
> eigenvalues with
> slepc (maybe using some trick)?

The actual slepc version (2.3.0) also offers a Lanczos
solver (for Hermitian problems) that can be used to compute the
smallest values in the spectrum (since I have been using
an older slepc version so far I have not tested this solver yet).
I have just commited some changes to also include the
Lanczos algorithm that comes with the current version.

For computing the smallest eigenvalues I have used slepc
(2.2.1) together with the arpack package, but it seems that
I need to change some cunfiguration stuff to get everything
working with the 2.3.0 version.

Steffen

=20
> In the meantime, I export the element matrices to a file and=20
> use external
> solver, pysparse
>=20
> http://people.web.psi.ch/geus/pyfemax/pysparse.html
>=20
> so I have a small (88 lines) python script, which assembles=20
> the global matrices
> (they are called A and B in libmesh), and calls Jacobi=20
> Davidson method from
> pysparse module. The solver is written in C (exported to=20
> python), it's fast and
> it works.=20
>=20
> Ondrej
>=20
> On Mon, Jan 16, 2006 at 12:25:50AM +0100, Steffen Petersen wrote:
> > Hello Michael,
> >=20
> > a few weeks ago you have asked for
> > solving generalized eigenvalue problems with libMesh.
> > Meanwhile, I have extended the slepc interface
> > to also support generalized problems
> > (with a few modifaications example 16
> > may be used for solving a generalized eigenvalue
> > problem).
> > Feel free to ask if you are interested in some
> > more details.
> >=20
> > Steffen
> >=20
> >=20
> >=20
> > Michael Povolotskyi schrieb:
> > >Dear Libmesh developers,
> > >I have to solve an eigenvalue problem for a quantum=20
> physics calculations.
> > >My questions are:
> > >1) Is it possible to solve a general eigenvalue problem=20
> like Hx =3D Sx,=20
> > >where H and S are known matrixes.
> > >2) Is it possible to have complex (self-conjugated) matrixes?
> > >
> > >Thank you,
> > >Michael.
> > >=20
> > >-------------------------------------------------------=20
> This SF.net=20
> > >email is sponsored by: Splunk Inc. Do you grep through log=20
> files for=20
> > >problems? Stop! Download the new AJAX search engine that=20
> makes searching=20
> > >your log files as easy as surfing the web. DOWNLOAD SPLUNK!=20
> > >http://ads.osdn.com/?ad_idv37&alloc_id=16865&op=3Dclick=20
> > >_______________________________________________=20
> Libmesh-users mailing=20
> > >list Lib...@li...=20
> > >https://lists.sourceforge.net/lists/listinfo/libmesh-users
> >=20
> >=20
> >=20
> > -------------------------------------------------------
> > This SF.net email is sponsored by: Splunk Inc. Do you grep=20
> through log files
> > for problems?  Stop!  Download the new AJAX search engine that makes
> > searching your log files as easy as surfing the  web. =20
> DOWNLOAD SPLUNK!
> > http://ads.osdn.com/?ad_id=3D7637&alloc_id=3D16865&op=3Dclick
> > _______________________________________________
> > Libmesh-users mailing list
> > Lib...@li...
> > https://lists.sourceforge.net/lists/listinfo/libmesh-users
>=20