Two-Dimensional Green's Function for Scattering and Radiation Problems in Elliptically-Layered Media

A recursive solution for the computation of the two-dimensional Green's function for the multilayer elliptic cylinder is reported. It is based on the scattering solution by this canonical scatterer through eigenfunction expansions in terms of Mathieu functions. The paper reports the mathematical details of the approach as well as several validation tests and comparisons.