Benjamin Gilvey's Outputs (2)

Quadrature methods for highly oscillatory singular integrals (2020)
Journal Article
Gao, J., Condon, M., Iserles, A., Gilvey, B., & Trevelyan, J. (2021). Quadrature methods for highly oscillatory singular integrals. Journal of computational mathematics, 39(2), 227-260. https://doi.org/10.4208/jcm.1911-m2019-0044

We address the evaluation of highly oscillatory integrals, with power-law and logarithmic singularities. Such problems arise in numerical methods in engineering. Notably, the evaluation of oscillatory integrals dominates the run-time for wave-enriche... Read More about Quadrature methods for highly oscillatory singular integrals.

Singular enrichment functions for Helmholtz scattering at corner locations using the Boundary Element Method (2019)
Journal Article
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

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... Read More about Singular enrichment functions for Helmholtz scattering at corner locations using the Boundary Element Method.