A Parallel Implementation of the Jacobi-Davidson Eigensolver and Its Application in a Plasma Turbulence Code

In the numerical solution of large-scale eigenvalue problems, Davidson-type methods are an increasingly popular alternative to Krylov eigensolvers. The main motivation is to avoid the expensive factorizations that are often needed by Krylov solvers when the problem is generalized or interior eigenvalues are desired. In Davidson-type methods, the factorization is replaced by iterative linear solvers that can be accelerated by a smart preconditioner. Jacobi-Davidson is one of the most effective variants. However, parallel implementations of this method are not widely available, particularly for non-symmetric problems. We present a parallel implementation to be released in SLEPc, the Scalable Library for Eigenvalue Problem Computations, and test it in the context of a highly scalable plasma turbulence simulation code. We analyze its parallel efficiency and compare it with Krylov-type eigensolvers.