A new procedure for solving multigroup neutron diffusion eigenvalue problems

The spatial distribution of neutron flux within the core of a nuclear reactor plays a crucial role in ensuring nuclear safety. The eigenvalue problem of neutron diffusion equations can be solved to determine this distribution. Typically, the fluxes are solved for one energy group at a time using the power iteration method, which helps reduce computational storage requirements. However, when dealing with energy groups that contain upscattering terms, it may be necessary to solve all energy groups simultaneously, resulting in larger matrix sizes and increased storage burden. To address this issue, this paper presents a precise and efficient boundary-type method called the Half-Boundary Method (HBM). HBM uses a hybrid variable to reduce the order of the differential equation and derives the relationship between variables at adjacent nodes through integration, thus obtaining the relationship between variables at any node and the unknowns at half-boundary. In order to further reduce the matrix order, HBM is combined with three iterative methods: the standard power iteration, accelerated power iteration with adaptive Wielandt shift, and energy group-coupling iteration. The results demonstrate that HBM requires less matrix storage compared to the Finite Difference Method (FDM). Consequently, HBM is particularly suitable for problems involving the upscattering terms. Furthermore, for heterogeneous problems, HBM naturally maintains continuity without the need for introducing new boundary conditions, thus saving storage requirements.