The electromagnetic scattering problem by a cylindrical doubly connected domain at oblique incidence: the direct problem

Abstract

We consider the direct electromagnetic scattering problem of time-harmonic obliquely incident waves by a infinitely long, homogeneous and doubly-connected cylinder in three dimensions. We apply a hybrid integral equation method (combination of the direct and indirect methods) and we transform the scattering problem to a system of singular and hypersingular integral equations. The well-posedness of the corresponding problem is proven. We use trigonometric polynomial approximations and we solve the system of the discretized integral operators by a collocation method.

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

“…From a mathematical point of view, the solution of the direct problem, analytical and numerical, needs special treatment even though it is based on classical techniques. This work adds to a series of papers dealing with direct scattering problems under similar conditions [7,11,12,15].…”

The scattering problem of obliquely incident electromagnetic waves by an inhomogeneous infinitely long cylinder

“…In this context, we investigate the scattering problem of obliquely incident electromagnetic waves by an infinitely long scatterer. This configuration has recently garnered significant interest, leading to numerous publications from both mathematicians and applied scientists, see for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

“…Additionally, they addressed the corresponding inverse problem, aiming to reconstruct the scatterer's shape [2,3]. In [6], the direct problem was examined for a doubly-connected cylinder. This year, the authors examined the direct problem for a cylinder with piecewise constant material parameters (electric permittivity and magnetic permeability) [15].…”