Towards high frequency boundary element methods for multiple scattering

Abstract

Standard Boundary Element Methods (BEM) for time-harmonic acoustics, using piecewise polynomial finite-element type approximation spaces, have a computational cost that grows rapidly with frequency, to ensure at least a fixed number of degrees of freedom per wavelength. Hybrid Numerical-Asymptotic (HNA) BEMs, based on enriched approximation spaces consisting of the products of piecewise polynomials with carefully chosen oscillatory functions, have a computational cost that is almost frequency-independent for some problem classes, but the technology is largely undeveloped for problems where multiple scattering is important. In this paper we present a computational method, supported by mathematical analysis, which suggests that multiple scattering configurations may be within reach. Specifically, we propose an algorithm to solve, by a HNA BEM, scattering by a pair of screens in an arbitrary configuration, which we anticipate may serve as a building block towards general multiple scattering problems with computational cost independent of frequency. The specific configuration considered, as we discuss, is relevant to the simulation of multiple outdoor noise barriers.