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A high frequency boundary element method for scattering by a class of multiple obstacles

Gibbs, A., Chandler-Wilde, S., Langdon, S. and Moiola, A. (2020) A high frequency boundary element method for scattering by a class of multiple obstacles. IMA Journal of Numerical Analysis. ISSN 1464-3642

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Abstract/Summary

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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:90420
Publisher:Oxford University Press

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