Andrew Gibbs

I am an applied mathematician working at University College London. Broadly speaking, my research focuses on the design, analysis and implementation of numerical models for acoustic and electro-magnetic wave propagation. These methods draw largely from approximation theory, complex analysis, asymptotic methods and functional analysis.

I am currently a named Co-Investigator on the project EP/V053868/1: Singular and Oscillatory Quadrature on Non-Smooth Domains, with Prof David Hewett.

In September 2023 I won the UKAN+ Mathematical Acoustics paper prize.

I am an early career rep for the Computational Acoustics Special Interest Group of the UK Acoustics Network (UKAN+). I currently maintain the knowledgebase, which was originally built by Amelia Gully.

Mathematical Software

PathFinder

Matlab/Octave package for efficient evaluation of oscillatory integrals in the class $\int_{a}^bf(x)\exp(\mathrm{i}\omega g(x)) \mathrm{d} x$ where $g$ is a polynomial, $\omega>0$ and $f$ is entire. The endpoints $a,b$ can be complex, even infinite.

IFSintegrals

Julia package for the approximation of integrals and integral equations posed on self-similar fractals $\Gamma$. The main requirement is that $\Gamma$ can be described by a set of affine contraction maps $s_m$, such that $\Gamma = \bigcup_{m=1}^M s_m(\Gamma).$ Specifically, these maps are $s_m(x) := A_m\rho_mx+\delta_m,$ where $A_m$ is a rotation/reflection matrix, $\delta_m$ is a translation and $\rho_m<1$ is a contraction.

HNA BEM LAB

Matlab package for solving the Helmholtz BVP \begin{align} (\Delta+\omega^2)u=0\quad\text{ in }\mathbb{R}^2\setminus\Omega\\ u=0\quad\text{on }\partial\Omega \end{align} where $\Omega$ is polygonal, or a (bounded) screen $\Omega\subset\mathbb{R}.$ The method requirs $O(1)$ DOFs for convex polygons or screens as $\omega\to\infty$, and has $O(1)$ computational cost for multiple aligned screens.

Under review

PhD

My PhD was supervised by Simon Chandler-Wilde, Stephen Langdon and Andrea Moiola. The thesis is available here.

MMath

My MMath dissertation was supervised by Zuowei Wang. It is available here.