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

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