A hybrid technique for the analysis of scattering by impedance wedges

Abstract

A non-metallic wedge is an important canonical geometry of the high-frequency diffraction theory. Unfortunately, neither pure analytical nor pure numerical approaches can solve the problem. Analytical methods fail because the boundary-value problems are typically non-separable. Application of the numerical techniques, like boundary integral equations or finite elements, is complicated by the infinite size of the scatterer and the singular behaviour of the solution at the edge. This paper presents a hybrid approach to the problem of diffraction of a plane obliquely incident electromagnetic wave by a wedge with impedance boundary conditions. The approach is based on an eigenfunction expansion of the solution and combines analytical construction of the expansion functions with numerical determination of the expansion coefficients.