Spatial modes for the neutron diffusion equation and their computation

Different spatial modes can be defined for the neutron diffusion equation such as the λ,α and γ-modes. These modes have been successfully used for the analysis of nuclear reactor characteristics. In this work, these modes are studied using a high order finite element method to discretize the equations and also different methods to solve the resulting algebraic eigenproblems, are compared. Particularly, Krylov subspace methods and block-Newton methods have been studied. The performance of these methods has been tested in several 3D benchmark problems: a homogeneous reactor and several configurations of NEACRP reactor.