Krylov subspace iteration for eigenvalue response matrix calculations

Recent work has revisited the eigenvalue response matrix method as an approach for reactor core analyses. In its most straightforward form, the method consists of a two-level Eigen problem. An outer Picard iteration updates the k-eigenvalue, while the inner Eigen problem imposes current continuity between coarse meshes. In this paper, several Eigen solvers are evaluated for this inner problem, using several 2-D diffusion benchmarks as test cases. The results indicate both the explicitly-restarted Arnoldi and the Krylov-Schur methods are up to an order of magnitude more efficient than power iteration. This increased efficiency makes the nested eigenvalue formulation more effective than the ILU-preconditioned Newton-Krylov formulation previously studied. (authors)