Measuring the effect of rounding the corners of scattering structures

In studying acoustic or electromagnetic wave diffraction, the choice of an appropriate canonical structure to model the dominant features of a scattering scenario can be very illuminating. A common approach used when dealing with domains with corners is to round the corners, producing a smooth surface, eliminating the singularities introduced by the corners. In order to quantify the effect of corner rounding, this paper examines the diffraction from cylindrical scatterers which possess corners, that is, points at which the normal changes discontinuously. We develop a numerical method for the scattering of a plane wave normally incident on such cylindrical structures with soft, hard, or impedance loaded boundary conditions. We then examine the difference between various test structures with corners and with the corners 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 point. We then examine the nature of the differences in the far field between the cornered and rounded scatterers as well as the effect on the differences as the frequency of the plane wave increases and obtain precise quantitative estimates for the rate of convergence of the maximum difference between the far-field solutions as the radius of curvature of the rounded scatterer approaches zero.