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.