My general interests are in Numerical Analysis and Scientific Computing.
I'm a participant in the UK "GungHo" Dynamical Core project (supported by NERC grants NE/I000747/1, NE/I016007/1, NE/I02013X/1, NE/K006789/1) which is a collaboration between the UK Met Office, university researchers from Imperial College London, Reading, Exeter, Bath, Leeds and Manchester, and computational scientists from STFC Daresbury. We are designing and building a dynamical core (the fluid dynamics component of a numerical weather prediction system) with the aim of achieving parallel scalability on the next generation of supercomputers. My own contributions are in designing numerical methods that can handle the multiscale features of atmospheric flows on pseudouniform grids, which avoid the inherent scalability bottleneck of the poles on a latitude-longitude grid. This has led to new numerical discretisations based on compatible finite elements (also known as finite element exterior calculus). At Imperial College we are testing out the performance (both from the point of view of ability to represent large scale atmospheric dynamics, and in terms of computational scalability and efficiency) within the Firedrake project. This work is also being supported through studentships provided by the Grantham Institute for Climate Change. I am also one of the co-Investigators of the Platform for Research in Simulation Methods at Imperial College, which is coordinating research in high-performance software for finite element methods across Mathematics, Computing, Aeronautics and Earth Science and Engineering.
I am also working on the problem of improving the predictability of fronts in numerical weather prediction models (supported by NERC grant NE/K012533/1 and an EPSRC CASE award with the UK Met Office). We have demonstrated that the numerical dissipation required to stabilise simulations of fronts near the frontal region causes large errors in the large scale balanced flow, thus reducing the ability of the model to predict future evolution (i.e., weather). It is hypothesised that this may be one of the reasons why deterministic forecast accuracy is limited to 7-10 days (rather than chaos, the usual explanation). We are now working on how to modify numerical schemes so that the numerical stabilisation does not damage forecast predictability in this manner.
I'm also interested in mathematical aspects of data assimilation, and have recently written a book on the topic in collaboration with Sebastian Reich, entitled "Probabilistic Forecasting and Bayesian Data Assimliation". This topic is one of the core themes of the Mathematics of Planet Earth Centre for Doctoral Training, of which I am the co-Director of Studies for the MRes year.
Some other topics I'm interested in include: numerical methods for diffeomorphic shape registration, geometric integration and variational integrators for fluid dynamics.
I also collaborate with Igor Shevchenko and Wei Pan who are PDRAs on the Stochastic Geophysical Fluid Dynamics EPSRC project led by Prof Darryl Holm.
SciCADE 17, University of Bath (invited talk), 11-15 Sept 2017.