A theoretical and numerical study of oblique scattering by an inhomogeneous cylinder

Abstract

We consider the solvability of the direct scattering problem of an obliquely incident time-harmonic electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. The three-dimensional problem described by the Maxwell’s equations reduces to a set of two-dimensional Helmholtz equations, but with the transmission conditions having also tangential derivatives of the fields. The ellipticity of the problem is proven through the Shapiro-Lopatinskij condition. Then, classical techniques can be used to prove the uniqueness and existence of the solution. For the numerical solution, we consider quadrature rules and we derive convergent representations for both the near- and far-fields.