A high frequency boundary element method for scattering by two-dimensional screens

We propose a numerical-asymptotic boundary element method for problems of time-harmonic acoustic scattering of an incident plane wave by a soundsoft two-dimensional (2D) screen. Standard numerical schemes have a computational cost that grows at least linearly with respect to the frequency of the incident wave. Here, we enrich our approximation space with oscillatory basis functions carefully designed to capture the high frequency behaviour of the solution. We show that in order to achieve any desired accuracy it is sufficient to increase the number of degrees of freedom only in proportion to the logarithm of the frequency, as the frequency increases, and for fixed frequency we demonstrate exponential convergence with respect to the number of degrees of freedom.