The Mathematical Institute, University of Oxford, Eprints Archive

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

Hewett, David Peter and Langdon, S. and Chandler-Wilde, S. N. (2013) A frequency-independent boundary element method for scattering by two-dimensional screens and apertures. Technical Report. IMAJNA. (Submitted)

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Abstract

We propose and analyse a hybrid numerical-asymptotic $hp$ boundary element method for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high frequency asymptotics of the solution. Our numerical results suggest that fi�xed accuracy can be achieved at arbitrarily high frequencies with a frequency-independent computational cost. Our analysis does not capture this observed behaviour completely, but we provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom $N$ increases, and that to achieve any desired accuracy it is sufficient to increase $N$ in proportion to the square of the logarithm of the frequency as the frequency increases (standard boundary element methods require $N$ to increase at least linearly with frequency to retain accuracy). We also show how our method can be applied to the complementary "breakwater" problem of propagation through an aperture in an infinite sound-hard screen.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1761
Deposited By: Lotti Ekert
Deposited On:19 Dec 2013 08:38
Last Modified:29 May 2015 19:27

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