[petsc-users] Preconditioners for a FEM model

[murat keçeli]

Hi Jifeng,

I think your application is suitable for the SIPs method, see attached
paper.  We have improved it recently, so that it can handle very
large (500k by 500k with more than 3.e7 nonzeros) sparse matrices.Current
version of SIPs is basically adding a second layer of parallelism on top of
SLEPc's shift and invert method. Let me or Hong Zhang (cc, the developer of
SIPs) know, if you would like to give it a try.

Murat Keceli


On Wed, Jul 2, 2014 at 4:46 PM, jifeng zhao <
jifengzhao2015 at u.northwestern.edu> wrote:

> Hello all,
>
> I am working on solving a generalized eigenvalue problem with SLEPC and
> PETSC.
>
> *K* x = lamda *M* x
>
> I attached the sparsity pattern of matrix *M* (*K* is the same). It is a
> FEM model. It is so sparse is because of constraints.
>
> I have tried two things:
>
> 1. Krylov-Schur and exact shift-and-invert (I will try MUMPS in future).
> It works. But I am worrying that it is less parrallelable, when the problem
> contains millions of degree of freedom.
>
> 2. JD with Jacobi preconditioner. It could work, but a lot of tuning needs
> to be done in terms of RTOL, max_iteration_number. And sometimes I suffer
> from a stagnated solution, and can't obtain accurate result.
>
> Does anybody know that for my specific case of matrix sparsity, is there
> any thing I can do to speed up my direct solver (Krylov-Schur)?
>
> Is there any recommended preconditioners I could try on, for the case of
> JD? There are a lot of preconditioners in HYPRE library.
>
> Thank you in advance!
> [image: Inline image 1]
> --
> Jifeng Zhao
> PhD candidate at Northwestern University, US
> Theoretical and Applied Mechanics Program
>
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