Diffraction of Acoustic Waves by a Wedge of Point Scatterers

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Abstract

This article 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, which allows us to compute the interaction of thousands of scatterers forming the wedge. A crucial aspect of this numerical procedure is the effective truncation of slowly convergent single and double infinite series, which requires careful asymptotic analysis. A convergence criterion is formulated and shown to be satisfied for a large class of physically interesting cases. A comparison to direct numerical simulations is made, highlighting the accuracy of the method.

Bibliographical metadata

Original languageEnglish
JournalSIAM Journal of Applied Mathematics
Volume82
Issue number3
DOIs
Publication statusPublished - 23 May 2022