Error estimation of the Method of Auxiliary Sources (MAS) for scattering from an impedance circular cylinder

The purpose of this paper is a rigorous error estimation of the Method of Auxiliary Sources (MAS), when the latter is applied to electromagnetic scattering from a circular, coated, perfectly conducting cylinder, assumed to satisfy the Standard Impedance Boundary Condition (SIBC). The MAS matrix is inverted analytically, via eigenvalue analysis, and an exact expression for the discretization error in the boundary condition is derived. Furthermore, an analytical formula for the condition number of the linear system is also extracted, in addition to an asymptotic estimate for large scatterers, explaining the irregular behavior of the computational error resulting from numerical matrix inversion. Finally, the optimal location of the auxiliary sources is determined, on the grounds of error minimization.