Functional Equations and Integral Equations in Spectral Domain for Scattering by Impedance Polygons

Some features of functional and integral equations involved in the spectral approach developed by the author (in Qu. J. of Mech. and Appl. Math., 59, 4, pp.517-550, 2006) for scattering by two-dimensional polygonal objects with arbitrary surface impedance conditions are presented. In this problem, the Wiener-Hopf method cannot be applied, while asymptotic methods can only be used if corners are widely spaced compared to wavelength, and the presence of imperfectly reflective surfaces particularly complicates the problem. After presenting our method to handle in a global manner the problem of n-part polygonal objects using the Sommerfeld-Maliuzhinets representation of the field, we detail the functional equations for the spectral functions, and the way to reduce them to a system of integral equations of the second kind with non-singular kernels, allowing approximations. We apply in particular this approach to the important class of three-part impedance polygons composed of a finite segment attached to two semi-infinite planes.