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
