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

[Thornquist, Heidi K]

Good point Alicia, I didn't pay enough attention to bcsstm01, that can
easily cause problems!

Andris, if M is indeed non-singular (it seems to be a diagonal in the spy
plot), would you mind trying this again with a generalized eigenproblem
that has a positive definite mass matrix?  For example, bcsst[k/m][6,8,9]?
 However, it may be easier to modify an example like
anasazi/epetra/example/BlockDavidson/BlockDavidsonEpetraExGenPrecIfpack.cpp
 or anasazi/epetra/example/LOBPCG/LOBPCGEpetraExGenPrecIfpack.cpp.  These
examples use a simple incomplete Cholesky preconditioner and will converge
to the solution with their current settings if the eigensolver sorts for
the smallest magnitude (--sort="SM").  Changing just the preconditioner,
from Ifpack to ML, will give you an easy problem to try it out on.

Thanks,
Heidi

-- 

Heidi K. Thornquist
Electrical Models & Simulation
Sandia National Laboratories
Albuquerque, NM  87185-1323





On 2/6/17, 10:59 AM, "Klinvex, Alicia Marie" <amklinv at sandia.gov> wrote:

>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
>
>??psalas iela 6a, R?ga
>00371 263 823 52
>andris.freimanis_1 at edu.rtu.lv
>www.rtu.lv
>