Optimization of the Method of Auxiliary Sources (MAS) for Scattering by an Infinite Cylinder Under Oblique Incidence

Abstract

This paper presents a rigorous accuracy analysis of the method of auxiliary sources (MAS) for the problem of oblique incidence plane wave scattering by a perfectly conducting, infinite circular cylinder. For this particular scattering geometry, it is shown that the MAS matrix is inverted analytically, via eigenvalue analysis, and an exact mathematical expression for the discretization error is derived. Furthermore, the computational error, resulting from numerical matrix inversion, is calculated and compared to the analytical one, showing perfect fit for a wide range of the auxiliary sources' locations. The irregular behavior of the computational error for small values of the auxiliary sources' radii is explained by the corresponding high values of the linear system's condition number. It is also demonstrated that specific source locations, associated with the characteristic eigenvalues of the scattering problem, should be avoided, because then both computational and analytical error increase very abruptly. The dependence of the computational and analytical error on the angle of incidence is thoroughly investigated. Finally, the optimal location of the auxiliary sources is determined on the grounds of error minimization.