Two-dimensional diffraction by structures with corners

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. This thesis examines and quantifies the effect of corner rounding both numerically and analytically. The diffraction from cylindrical scatterers which possess corners, that is, points at which the normal changes discontinuously is examined. 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 both in the frequency and the time domain. We 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 and verify them analytically. Having examined the near- and far-field solutions we confirm that the techniques employed also produce highly accurate solutions in close proximity to the surface of the scatterer especially in the vicinity of the corner. Our study of the effect of corner rounding is extended to arrays of scatterers using a classical but computationally intensive method for these calculations. To enable the study of larger scatterer arrays, we employ the recently available TMATROM an object-oriented T-matrix software package,with our own forward solvers.