Gilvey, B.D. and Trevelyan, J. and 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). pp. 519-533.
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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.1002/nme.6232|
|Publisher 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.|
|Date accepted:||04 September 2019|
|Date deposited:||05 September 2019|
|Date of first online publication:||24 October 2019|
|Date first made open access:||24 October 2020|
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