Title: Diffraction and resonance of acoustic waves by a wedge of point scatterers

Matthew A. Nethercote,. School of Mathematics, University of Manchester, Oxford Road, Manchester,, UK

Abstract: This talk considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete Wiener-Hopf technique. An effective and accurate iterative numerical procedure is developed to solve the diffraction problem. A crucial aspect of this numerical procedure is the effective truncation of slowly convergent single and double infinite series, which requires careful asymptotic analysis. Some convergence criteria is formulated and a comparison to direct numerical simulations is made, highlighting the accuracy of the method.

Following this, the topic will turn to the special case of resonance in this configuration. Specifically, the aim is to understand the effect of the coupling between the two arrays when resonance occurs. A brief overview on resonance for infinite and semi-infinite arrays is given, with an improved uniform far-field approximation during one of the more difficult resonance cases.