A Hierarchical Domain Decomposition Boundary Element Method Applied to the Multiregion Problems of Neutron Diffusion Equations

A technique is presented for solving neutron diffusion equations with the boundary element method (BEM) based on a hierarchical domain decomposition technique. In this method, the reactor domain is decomposed into homogeneous regions and the boundary condition on the common boundary of regions is initially assumed. The neutron diffusion equation is solved iteratively at two levels of hierarchical structure: First, BEM is applied to solve the neutron diffusion equation of each homogeneous region under the given assumed boundary conditions and an assumed multiplication factor. Then, these assumed values are modified to satisfy the continuity conditions for the neutron flux and neutron current.

The proposed technique is useful for multiregion problems with a large number of regions of complex geometry, where the finite difference approximation cannot be applied properly.