A high frequency boundary element method for scattering by a class of multiple obstacles
Abstract
We propose a boundary element method for problems of time-harmonic acoustic scattering by multiple obstacles in two dimensions, at least one of which is a convex polygon. By combining a Hybrid Numerical Asymptotic (HNA) approximation space on the convex polygon with standard polynomial-based approximation spaces on each of the other obstacles, we show that the number of degrees of freedom required in the HNA space to maintain a given accuracy needs to grow only logarithmically with respect to the frequency, as opposed to the (at least) linear growth required by standard polynomial-based schemes. This method is thus most effective when the convex polygon is many wavelengths in diameter and the small obstacles have a combined perimeter comparable to the problem wavelength.
Cite
@article{arxiv.1903.04449,
title = {A high frequency boundary element method for scattering by a class of multiple obstacles},
author = {Andrew Gibbs and Simon Chandler-Wilde and Stephen Langdon and Andrea Moiola},
journal= {arXiv preprint arXiv:1903.04449},
year = {2020}
}