Diffraction of acoustic waves by multiple semi-infinite arraysa).

Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate. However, there are some strict limitations to its use, usually the boundary conditions need to be imposed on parallel lines (after a suitable mapping).

The Wiener-Hopf technique, its generalizations and applications: constructive and approximate methods.

This paper reviews the modern state of the Wiener-Hopf factorization method and its generalizations. The main constructive results for matrix Wiener-Hopf problems are presented, approximate methods are outlined and the main areas of applications are mentioned. The aim of the paper is to offer an overview of the development of this method, and demonstrate the importance of bringing together pure and applied analysis to effectively employ the Wiener-Hopf technique.

A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics.

Many problems in fluid mechanics and acoustics can be modelled by Helmholtz scattering off poro-elastic plates. We develop a boundary spectral method, based on collocation of local Mathieu function expansions, for Helmholtz scattering off multiple variable poro-elastic plates in two dimensions. Such boundary conditions, namely the varying physical parameters and coupled thin-plate equation, present a considerable challenge to current methods.

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

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.