Matrix-type higher order fundamental solutions to three-dimensional two-group neutron diffusion equations

摘要

The zero-order and the higher-order fundamental solutions for the 3-D two-group neutron diffusion equations have been derived in such a way that these solutions satisfy the first and the second group equations simultaneously. Each degree of the solutions has a 2×2 matrix form based on two types of function, r~p exp(-iBr) and r~p exp (-kr). Singularities of type (1/r) are only found at the diagonal components of the zero-order solutions; however, no singularities are found at any components of the higher-order solutions. These solutions can be used for applying the multiple reciprocity boundary element method to 2-D two-group neutron diffusion problems.