# Numerical-asymptotic boundary integral equation methods for high frequency scattering problems

**Speaker:** Simon Chandler-Wilde (Department of Mathematics and Statistics, University of Reading)

**Title:** Numerical-asymptotic boundary integral equation methods for high frequency scattering problems

**Abstract:** Boundary integral/boundary element methods are a computational method of choice for wave scattering problems in acoustics and electromagnetics as low to moderate frequencies. But they require prohibitively large computational resources at high frequencies (corresponding to small wavelengths) because of the need for a very fine discretisation to resolve the solution on the surface of the scatterer, since this solution oscillates rapidly on the scale of the wavelength. At high frequencies asymptotic methods, for example Keller’s geometrical theory of diffraction, are an attractive alternative, but have limited and difficult to quantify accuracy. I’ll give an overview of progress that has been made on combining these approaches, using oscillatory boundary element basis functions that incorporate asymptotic high frequency information. These numerical-asymptotic methods achieve, for many classes of scattering problem, high accuracy at a fraction of the computational cost of standard numerical methods.