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A wavenumber independent boundary element method for an acoustic scattering problem

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Langdon, S. and Chandler-Wilde, S. N. (2006) A wavenumber independent boundary element method for an acoustic scattering problem. SIAM Journal on Numerical Analysis (SINUM), 43 (6). pp. 2450-2477. ISSN 0036-1429

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Abstract/Summary

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:4902
Uncontrolled Keywords:Galerkin method high frequency Helmholtz equation WEAK VARIATIONAL FORMULATION FAST MULTIPOLE METHOD HELMHOLTZ-EQUATION MICROLOCAL DISCRETIZATION SOUND-PROPAGATION IMPEDANCE PLANE NUMERICAL QUADRATURE SURFACE IMPEDANCE FINITE-ELEMENTS HALF-PLANE
Publisher:Society for Industrial and Applied Mathematics
Publisher Statement:Copyright © 2006, Society for Industrial and Applied Mathematics

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