Optimized Eigenvalue Solvers for the Neutron Transport Equation

Abstract

A discrete ordinates method has been developed to approximate the neutron transport equation for the computation of the lambda modes of a given configuration of a nuclear reactor core. This method is based on discrete ordinates method for the angular discretization, resulting in a very large and sparse algebraic generalized eigenvalue problem. The computation of the dominant eigenvalue of this problem and its corresponding eigenfunction has been done with a matrix-free implementation using both, the power iteration method and the Krylov-Schur method. The performance of these methods has been compared solving different benchmark problems with different dominant ratios.