Singular enrichment functions for Helmholtz scattering at corner locations using the boundary element method
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Publication Date
2020-02-15Journal Title
International Journal for Numerical Methods in Engineering
ISSN
0029-5981
Publisher
Wiley
Volume
121
Issue
3
Pages
519-533
Type
Article
This Version
AM
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Gilvey, B., Trevelyan, J., & Hattori, G. (2020). Singular enrichment functions for Helmholtz scattering at corner locations using the boundary element method. International Journal for Numerical Methods in Engineering, 121 (3), 519-533. https://doi.org/10.1002/nme.6232
Abstract
In this paper we use an enriched approximation space for the efficient and accurate solution of the Helmholtz equation in order to solve problems of wave scattering by polygonal obstacles. This is implemented in both Boundary Element Method (BEM) and Partition of Unity Boundary Element Method (PUBEM) settings. The enrichment draws upon the asymptotic singular behaviour of scattered fields at sharp corners, leading to a choice of fractional order Bessel functions that complement the existing Lagrangian (BEM) or plane wave (PUBEM) approximation spaces. Numerical examples consider configurations of square scattering objects, subject to the Neumann ‘sound hard’ boundary conditions, demonstrating that the approach is a
suitable choice for both convex scatterers and also for multiple scattering objects that give rise to multiple reflections. Substantial improvements are observed, significantly reducing the number of degrees of freedom required to achieve a prescribed accuracy in the vicinity of a sharp corner.
Identifiers
External DOI: https://doi.org/10.1002/nme.6232
This record's URL: https://www.repository.cam.ac.uk/handle/1810/296743
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