Singular enrichment functions for Helmholtz scattering at corner locations using the Boundary Element Method

Gilvey, B.D.; Trevelyan, J.; Hattori, G.

doi:10.1002/nme.6232

Singular enrichment functions for Helmholtz scattering at corner locations using the Boundary Element Method

Gilvey, B.D.; Trevelyan, J.; Hattori, G.

Authors

Benjamin Gilvey benjamin.gilvey@durham.ac.uk
PGR Student Doctor of Philosophy

Professor Jon Trevelyan jon.trevelyan@durham.ac.uk
Emeritus Professor

G. Hattori

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 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.

Citation

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

Journal Article Type	Article
Acceptance Date	Sep 4, 2019
Online Publication Date	Oct 24, 2019
Publication Date	Feb 15, 2020
Deposit Date	Sep 5, 2019
Publicly Available Date	Oct 24, 2020
Journal	International Journal for Numerical Methods in Engineering
Print ISSN	0029-5981
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	121
Issue	3
Pages	519-533
DOI	https://doi.org/10.1002/nme.6232

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Copyright Statement
This is the accepted version of the following article: Gilvey, B.D., 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 which has been published in final form at https://doi.org/10.1002/nme.6232. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for self-archiving.