Applying an iterative method numerically to solve n × n matrix Wiener-Hopf equations with exponential factors

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2020-01, Vol.378 (2162), p.20190241-20190241
• Main Authors: Priddin, Matthew J, Kisil, Anastasia V, Ayton, Lorna J
• Format: Article
• Language: English
• ISSN: 1364-503X; 1471-2962
• DOI: 10.1098/rsta.2019.0241

This paper presents a generalization of a recent iterative approach to solving a class of 2 × 2 matrix Wiener-Hopf equations involving exponential factors. We extend the method to square matrices of arbitrary dimension , as arise in mixed boundary value problems with junctions. To demonstrate the method, we consider the classical problem of scattering a plane wave by a set of collinear plates. The results are compared to other known methods. We describe an effective implementation using a spectral method to compute the required Cauchy transforms. The approach is ideally suited to obtaining far-field directivity patterns of utility to applications. Convergence in iteration is fastest for large wavenumbers, but remains practical at modest wavenumbers to achieve a high degree of accuracy. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.