[Trilinos-Users] [EXTERNAL] Anasazi solver with ML preconditioner won't converge

[Klinvex, Alicia Marie]

Heidi,

Is it possible he's seeing some goofy behavior because the M in that small problem is singular?  Maybe it would be worth trying again with a problem where M is nonsingular, since Andris's problem of interest sounds like it will have a nonsingular M.

- Alicia

-----Original Message-----
From: Trilinos-Users [mailto:trilinos-users-bounces at trilinos.org] On Behalf Of Andris Freimanis
Sent: Friday, February 3, 2017 10:50 AM
To: Thornquist, Heidi K <hkthorn at sandia.gov>; Tuminaro, Raymond S <rstumin at sandia.gov>; trilinos mailing list <trilinos-users at trilinos.org>
Subject: Re: [Trilinos-Users] [EXTERNAL] Anasazi solver with ML preconditioner won't converge

Heidi,

yes, I used those two matrices only as a test. Actual matrices will be real SPD and much larger. An example of a small problem would be two
37'500x37'500 size matrices, K with 7'916'526 elements and M with 37'500 elements. I don't know if it helps, but I attached structure plots.

LOBPCG does seem like a better choice, as matrices will be large and I'll only need few (20-30 max) smallest eigenpairs. I rewrote my code and tried running it for 1 eigenpair with the same 48x48 matrices, LOBPCG also doesn't converge. I attached output and main.cpp file. Could this be because matrices are too small for this method?


2017.02.02. 19:57, Thornquist, Heidi K wrote:
> Hi Ray and Andris,
>
> I believe that the test matrix is the BCSSTK01/BCSSTM01 matrix pair 
> from the BCSSTRUC1 set in Matrix Market.  That was just a guess from 
> the statistics.  The convergence of this matrix pair can be affected 
> by many things, including which eigenvalues you are looking for, the 
> size of subspace, and the number of allowed iterations.  I think that 
> the inclusion of the ML preconditioner may be obfuscating the issue.  
> It's easiest to reduce the complexity of the possibilities (i.e. 
> remove the
> preconditioner) and see if you can something to converge for the 
> simplest case, especially when the problem is so small.  Then start 
> adding preconditioning, spectral transformations, etc. to speed up the 
> solve and build more intuition about the solver.
>
> Since you are looking for the smallest eigenvalues and the system is 
> SPD, have you also considered using LOBPCG?  Is this exercise with the 
> Matrix Market test matrices in anticipation of a larger generalized 
> eigenproblem with SPD matrices?  We can give guidance on how to solve 
> this eigenproblem, but knowing what your final target will help us out.
>
> Thanks,
> Heidi
>

--
Andris Freimanis
PhD student

Riga Technical university
Institute of transporation
engineering

Ķīpsalas iela 6a, Rīga
00371 263 823 52
andris.freimanis_1 at edu.rtu.lv
www.rtu.lv