Calculating the Discrete Spectrum of the Transport Operator with Arbitrary Order Anisotropic Scattering

Abstract

We consider here the numerical determination of the discrete spectrum of the neutron transport operator in a homogeneous subcritical infinite medium in the case of highly anisotropic scattering. Under mild assumptions on the scattering coefficients, one knows that the discrete spectrum is a finite set whose elements are real with absolute values larger than 1. Under these assumptions, we describe a method to compute all eigenvalues for an arbitrary order of anisotropic scattering. The method has been implemented in a C++ library using IEEE double precision arithmetic, allowing for fast calculations. Numerical results are compared to values in literature and to high‐precision calculations using Maple.