Application of the hierarchical domain decomposition boundary element method to the simplified P3 equation

Abstract In this paper, the hierarchical domain decomposition boundary element method (HDD-BEM), which has been developed to solve the diffusion equation, is applied to the simplified P 3 (SP 3 ) equation. The HDD-BEM solution for the SP 3 equation is provided in the present paper. A computer program, ABEMIE, based on the HDD-BEM is developed, and a two-dimensional one-group anisotropic-scattering benchmark problem is solved with it to verify the present HDD-BEM for the SP 3 equation. Through numerical benchmarking, it is shown that the present method results in good agreement with the solution obtained using the existing SP N solver based on the finite element method for both eigenvalue and neutron flux distribution. This benchmark result suggests that the HDD-BEM is suitable for application to the SP N equation.