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

Abstract

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 n, as arise in mixed boundary value problems with n 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)’.