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Towards high frequency boundary element methods for multiple scattering

Phillips, O., Chandler-Wilde, S. and Langdon, S. (2022) Towards high frequency boundary element methods for multiple scattering. In: Inter-noise 2022, 21-24 August 2022, Glasgow.

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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.

Item Type:Conference or Workshop Item (Paper)
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:105536


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