Regularizing Helmholtz–Galerkin technique in the plane-wave scattering from a finite set of coplanar thin circular resistive discs

This paper deals with the plane-wave scattering from a finite set of coplanar thin circular resistive discs in free space, i.e. discs of high conductivity materials with thicknesses very small with respect to the discs’ radii and the free-space wavelength. The scatterers are modelled as planar surfaces and suitable resistive boundary conditions for the fields. The unique solvable boundary value problem for Maxwell’s equation, established providing edge and radiation conditions for the fields, is recast as an infinite system of singular integral equations for the vector Hankel transform of the surface irrotational and solenoidal parts of the azimuthal harmonics of the effective surface current densities on the discs. The choice of orthonormal eigenfunctions of the most singular part of the integral operator exhibiting the behaviour of the unknowns as expansion functions in a Galerkin scheme leads to a fast-converging Fredholm second-kind matrix equation in l2 with symmetries and vanishing elements. Analytical techniques in the complex plane are used to represent the matrix coefficients in terms of quickly evaluable proper integrals of bounded continuous functions. Numerical results and comparisons with CST Microwave Studio (CST-MWS) are provided to show the effectiveness of the proposed method. This article is part of the theme issue ‘Analytically grounded full-wave methods for advances in computational electromagnetics’.