Half-Space Albedo Problem for Linear-Triplet Anisotropic Scattering with the H _N and SVD Methods

We examine the effect of linear-triplet anisotropic scattering on the solution of transport problems. We consider the albedo problem for a semi-infinite slab with a non-negative scattering kernel that is a linear combination of “linear” and “triplet” scattering. We use two different methods, both of which are based on Case method of singular eigenfunctions, namely the HN method and the SVD method. Case’s eigenfunctions and their orthogonality relations are derived and are used to solve the half-space albedo problem. The results of two methods are in agreement with each other and show that the triplet scattering has only a marginal effect on the solution of the transport problem while the linear scattering has a dominant role. Surprisingly this is true even when the strength of the linear scattering is small. We also report an improvement of the SVD method that allows us to refine the mesh as we please.