The effect of rounding the corners of scattering structures: E-polarisation case

In studying electromagnetic wavabout:newtabe diffraction from scatterers with corners, a common approach is to first round the corners, thus producing a smooth surface, and eliminating the singularities introduced by the corners. Numerical methods based upon integral equation formulations can then be readily applied. In order to quantify the effect of such corner rounding we examine the two-dimensional case of diffraction from cylindrical scatterers which possess corners, that is, points at which the normal changes discontinuously. We employ a numerical method for the scattering of a E-polarised plane wave normally incident on a perfectly conducting cylindrical structures of constant cross-section and which may include corners. We assess the impact on near- and far-field scattering, as a function of the radius of curvature in the vicinity of the rounded corner point. We conclude by quantifying the rate of convergence of the maximum difference between the far-field solutions as that radius of curvature of the rounded scatterer approaches zero.