A. Gibbs, D. P. Hewett, D. Huybrechs. **Numerical evaluation of oscillatory integrals via automated steepest descent contour deformation.** J. Comput. Phys., 501, (2024), arxiv preprint.

J. R. Ockendon, H. Ockendon, R. H. Tew, D. P. Hewett, A. Gibbs. **A caustic terminating at an inflection point.** Wave Motion, 125, (2024), arxiv preprint.

A. Gibbs, D. P. Hewett, B. Major. **Numerical evaluation of singular integrals on non-disjoint self-similar fractal sets.** Numer. Algorithms (2024), arxiv preprint.

A. Gibbs, D. P. Hewett, A. Moiola. **Numerical quadrature for singular integrals on fractals.** Num. Alg. 1-54, (2022), arxiv preprint.

J. Bannister, A. Gibbs, D. P. Hewett. **Acoustic scattering by impedance screens/cracks with fractal boundary: well-posedness analysis and boundary element approximation.** Math. Mod. Meth. Appl. Sci. 32(2), (2022), arxiv preprint.

A. Gibbs, D. Hewett, D. Huybrechs, E. Parolin. **Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation.** SN Partial Differ. Equ. Appl. 1(4):21, (2020), arxiv preprint.

A. Gibbs, S. Langdon, A. Moiola and S.N. Chandler-Wilde. **A high frequency boundary element method for scattering by a class of multiple obstacles.** IMA JNA 41(2), (2021), arxiv preprint.

A. Gibbs, S. Langdon, A. Moiola. **Numerically stable computation of embedding formulae for scattering by polygons (technical report).**

S.N. Chandler-Wilde, E.A. Spence, A. Gibbs, V. P. Smyshlyaev. **High-frequency bounds for the Helmholtz equation under parabolic trapping and applications in numerical analysis.**SIAM J. Math. Anal., 52(1), (2020),, arxiv preprint.