Solution of 3D multigroup, linearly anisotropic scattering, criticality problems by the AN boundary-element response-matrix method

A short summary devoted to the origin and the development of the AN method, as well as its relationship with the simplified spherical harmonics (SPN) method, is given. Attempts have been made to derive the AN partial differential equations and the related interface and boundary conditions as much as possible from first principles. The theory developed in previous works is extended to many energy groups and includes a rigorous treatment of the linearly anisotropic scattering. It is shown that also in this extended framework the AN differential equations can be transformed into a set of boundary integral equations that can be given a partial current form. This allows for a natural application of the response matrix method, a technique that is particularly suitable for application to large multiregion systems. The calculation procedures have been implemented into a computer code (BERM-AN). Solutions of a 2D and 3D cartesian coordinates multigroup criticality problems, with different AN approximations, are compared with those obtained by well assessed reference codes such as DORT, TORT and MCNP.