What effect does rounding the corners have on diffraction from structures with corners?

In studying electromagnetic wave diffraction, the choice of an appropriate canonical structure is significant in elucidating the dominant features of a scattering scenario. This study was originally motivated by the influence that the corners of buildings and their surface cladding might have on the wave propagation. When an integral equation approach is employed as the basis of numerical studies of the scattering of plane waves by an obstacle, a common technique for dealing with domains with corners is to round the corners. In order to clarify the effect of such corner rounding, this work examines the diffraction from cylindrical scatterers which possess corners, that is, points at which the normal changes discontinuously. Specifically we develop a numerical method for the scattering of an E- polarised plane wave by such cylindrical structures. We examine three different boundary conditions: soft, hard and an impedance loaded boundary condition, each enforced at all points on the cross-sectional boundary of the cylinder. We quantify the difference between test structures with corners and similar structures where the corners have been rounded to assess the impact on near- and far-field scattering, as a function of the radius of curvature in the vicinity of the rounded corner points.