Parallel shooting solution of the neutron transport equation in spherical geometry

Abstract

A direct and efficient parallel-shooting method is given for the solution of the spherical harmonics approximation to the neutron transport equation in spherical geometry with arbitrary anisotropic scattering and source. The special numerical difficulties due to the singularity at the center of the sphere are solved in a simple and efficient way. The algorithm “measures” the roundoff instability of the problem and eliminates it by performing a minimum of matrix transformations that ensure the linear independence of the matrix columns.