All Outputs (5)

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.

A comparison of high-order and plane wave enriched boundary element basis functions for Helmholtz problems (2020)
Journal Article
Gilvey, B., & Trevelyan, J. (2021). A comparison of high-order and plane wave enriched boundary element basis functions for Helmholtz problems. Engineering Analysis with Boundary Elements, 122, 190-201. https://doi.org/10.1016/j.enganabound.2020.10.008

When undertaking a numerical solution of Helmholtz problems using the Boundary Element Method (BEM) it is common to employ low-order Lagrange polynomials, or more recently Non-Uniform Rational B-Splines (NURBS), as basis functions. A popular alternat... Read More about A comparison of high-order and plane wave enriched boundary element basis functions for Helmholtz problems.

A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem (2020)
Journal Article
Carrer, J., Solheid, B., Trevelyan, J., & Seaid, M. (2021). A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem. Engineering Analysis with Boundary Elements, 122, 132-144. https://doi.org/10.1016/j.enganabound.2020.10.017

This work presents a boundary element method formulation for the solution of the anomalous diffusion problem. By keeping the fractional time derivative as it appears in the governing differential equation of the problem, and by employing a Weighted R... Read More about A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem.

Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures (2020)
Journal Article
Gong, Y., Dong, C., Qin, F., Hattori, G., & Trevelyan, J. (2020). Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures. Computer Methods in Applied Mechanics and Engineering, 367, Article 113099. https://doi.org/10.1016/j.cma.2020.113099

The isogeometric boundary element method (IGABEM) has great potential for the simulation of elasticity problems because of its exact geometric representation and good approximation properties. These advantages can be extended to thin structures, incl... Read More about Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures.

The Boundary Element Method applied to the solution of the Diffusion-Wave problem (2020)
Journal Article
Carrer, J., Solheid, B., Trevelyan, J., & Seaid, M. (2020). The Boundary Element Method applied to the solution of the Diffusion-Wave problem. Engineering Analysis with Boundary Elements, 117, 13-25. https://doi.org/10.1016/j.enganabound.2020.03.027

A Boundary Element Method formulation is developed for the solution of the two-dimensional diffusion-wave problem, which is governed by a partial differential equation presenting a time fractional derivative of order α, with 1.0 < α < 2.0. In the pro... Read More about The Boundary Element Method applied to the solution of the Diffusion-Wave problem.