Abstract

This talk will be split into two parts.

Firstly, I will talk about the situation when boundary conditions are given on many plates and the associated Wiener-Hopf equation. The Wiener-Hopf method can be considered as a Riemann-Hilbert method with added analytisity information allowing for full power of complex analysis methods to be exploited. I will explain the difficulties involved when matrix Wiener-Hopf equations are solved. I will describe how recent advances in computation of rational approximations and orthogonal polynomials can be used. The corresponding canonical acoustics scattering problems will be considered.
This is joint work with Matthew J. Priddin and Lorna J. Ayton.

Secondly, I will talk about how special functions called Mathieu function can be used to solve Helmholz equation with boundary conditions given on a plate. This allows to produce a fast and stable code for challenging conditions like varying elasticity and porosity on a plate. This is joint work with Matthew J. Colbrook.