Research Interests

I am interested in the modelling, theory, application and computation of nonlinear problems (linear problems are for cissies) with special interest in problems which arise in industry and the environment.

Adaptive moving mesh methods , with applications in meteorology and modelling climate
COVID-19 related modelling, including modelling the impact of COVID-19 on retail, HE, rail and tourism.
Data assimilation methods, with applications in meteorology and climate
(Digital) signal and image processing. Inverse problems including saving the whales
The mathematics of machine learning
Nonlinear elliptic and parabolic partial differential equations, especially problems with singularities.
Non-smooth dynamical systems (with applications to climate and machine learning) see my book on Piecewise-smooth Dynamical Systems: Theory and Applications,
Industrial and interdisciplinary applied mathematics
Geometric integration and its applications.
Optimal transport methods (with applications to mesh generation, propagation and machine learning)
Numerical weather and climate prediction
Power electronics

I also have a very strong interest in interdisciplinary projects closely linked to applications ranging from geology to micro-wave cooking and from digestion to folk dancing.
I am keen to take on PhD students in any of these areas. They can join my fabulous group of PhD students all involved in research in industrial maths and/or environmental sciences.

Current PhD Projects

Raising the roof . NERC PhD. Matt Griffith, Nick Mitchell, Met Office
Non-smooth models for climate Botswana PhD Kgomotso Susan Morupisi
Indoor LTE and WiFi propagation ICASE PhD. Hayley Wragg, Keith Briggs (BT)
Inverse problems in EEG Shaerdan Shataer
Surge in turbochargers Samba/IAAPS PhD. Kate Powers, Chris Brace, Paul Milewski, Colin
Mitigation zones for seismic surveys and marine animals KTP/PhD Guillermo Jimenez Arranz, Phillipe Blondel, SEICHE
Adaptive mesh methods for the shallow water equations Simone Appela, Tristan Pryer, Met Office
Machine learning for CME predications Chinese PhD Scholarship, Tina Zhou, Tom Haines, Met Office
Impact of climate change on cocoa farming Samba PhD. Tosin Babasola, CRIN
Inverse problems in ocean acoustics NPL funded PhD, Gianluca Audone, Matt Nunes, Phillipe Blondel, NPL

Current/recent PDRA Research Projects

MIVOR: Impact of climate change on the National Grid NGC funded. Beate Erhardt, Mixhong ??, Ghenghong Gu, NGC
Machine learning for hip fracture detection Arthritis Society, Beate Erhardt, Richie Gill
Moving meshes on the sphere with applications to weather prediction NERC
Along with Victor Galaktionov and Johannes Zimmer I was coordinator of the Bath Node of the FIRST (Fronts and Interfaces in Science and Technology) Marie Curie training network. See FIRST Network for more information about the project, workshops and positions.