[petsc-users] Preconditioners for a FEM model

[jifeng zhao]

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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