Dr. Andrew Gibbs - UCL

Department of Mathematics 25 Gordon Street London WC1H 0AY UK

Email address: andrew.gibbs@ucl.ac.uk

Research interests:

Most of my research is aimed at developing and analysing new techniques for solving wave scattering problems. In particular, my focus is on high frequency problems, and rough obstacles. My areas of interest can be split roughly into the following:

• Numerical analysis

• Asymptotic methods

• Highly oscillatory quadrature

• Boundary Element Methods

  Here is a link to my github page.

Papers:

• 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., volume 52, issue 1, pages 845-893 (2020), arxiv copy.

• A. Gibbs, S. Langdon and A. Moiola. Numerically stable computation of embedding formulae for scattering by polygons (arxiv preprint, under review).

• 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, arxiv copy.

• 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., arxiv copy.

• 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. (M3AS), arxiv copy

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

• A. M. Caetano, S. N. Chandler-Wilde, A. Gibbs, D. P. Hewett, A. Moiola, A Hausdorff-measure boundary element method for acoustic scattering by fractal screens (arxiv preprint, under review)

• A. Gibbs, D. P. Hewett, B. Major, Numerical evaluation of singular integrals on non-disjoint self-similar fractal sets, (arxiv preprint, under review)

Refereed Conference Proceedings:

• A. Gibbs, D. Huybrechs and D. P. Hewett. PathFinder: a toolbox for oscillatory quadrature, Proceedings of Waves 2019, Vieanna, August 2019.

• A. Gibbs, D. Huybrechs. A new toolbox for highly oscillatory and singular integrals, Proceedings of IABEM 2018, Paris, June 2018.

• A. Gibbs, S. Langdon and A. Moiola. Stable implementation of embedding formulae for computation of far field patterns, Proceedings of Waves 2017, Minnesota, May 2017.

• A. Gibbs, S. N. Chandler-Wilde, S. Langdon and A. Moiola. Hybrid numerical asymptotic approximation for multiple scattering problems, Proceedings of Waves 2015, Karlsruhe, Germany, July 2015.

Hertz

PhD thesis