My general interests are in Numerical Analysis and Scientific Computing.
- Compatible finite element methods for atmosphere and ocean simulation. In 2012, Jemma Shipton and I proposed using compatible finite elements (my term for finite element methods built around the finite element exterior calculus - I use this term to communicate with applications scientists) for geophysical fluid dynamics because of the special wave propagation and conservation properties that they provide. These ideas have been incorporated into the "Gungho" dynamical core being developed at the Met Office (including by my graduated PhD student, Thomas Bendall) for their next generation climate and weather model. My work has two streams, one on designing methods that conserve energy/enstrophy/other quantities, and one on practical issues of how to build a useable tool for weather and climate simulation (iterative solvers for implicit systems, limiters, unwinding etc.) Hopefully in the future these two streams will combine!
(participating current and recent group members: Werner Bauer, Jemma Shipton, Golo Wimmer, Thomas Gibson, Thomas Gregory, Hiroe Yamazaki, and Karina Kowalczyk.)
- Averaging methods for oscillatory PDEs. In research funded by EPSRC in collaboration with Beth Wingate, Jemma Shipton and Werner Bauer, I have been investigating numerical phase averaging techniques that use parallel computation to take large stable timesteps whilst minimising impact on accuracy.
(participating current and recent group members: Werner Bauer, Jemma Shipton, and Hiroe Yamazaki.)
- Parallel-in-time methods. Parallel-in-time methods are time stepping methods that make use of parallel processing in the time domain (as well as the space domain). The challenge is to produce methods that have additional parallel scalability and performance than those that use spatial domain decomposition alone. Previously funded by NERC and currently funded by ExCALIBUR via the Met Office (in a larger team on this topic with Beth Wingate, Jemma Shipton, David Moxey and Chris Cantwell), I am looking at how the Parallel-in-time technique referred to as "ParaDiag II" can be applied to geophysical fluid models building up to atmospheric dynamical cores. In this work we have developed a library, asQ, that facilitates use of this techniques for PDE models developed in Firedrake. With Jon Hill, in work funded by EPSRC, I am also investigating the application of Paradiag II to stratigraphic models that describe the formation of sedimentary rock over geological timescales.
(participating current and recent group members: Werner Bauer, Abdalaziz Hamdan, Joshua Hope-Collins, and Jemma Shipton.)
- Data assimilation algorithms. In research funded by EPSRC in collaboration with Dan Crisan, we are developing new particle filters (ensemble based methods for blending data and models rigorously) that incorporate optimisation algorithms to "nudge" the ensemble members towards the data before consistently correcting the weights using Girsanov's Theorem.
(participating group members: Maneesh Kumar Singh)
- Firedrake is an automated system for the solution of partial differential equations using the finite element method, led by David Ham. With David I am co-supervising two PhD students. Reuben Nixon-Hill is developing techniques to automate interaction between models (especially environmental models) and data, in particular automating the interpolation of discretised data to arbitrary points and their coupling in equation systems and optimisation tools. Sophia Vordewuelbecke is developing matrix-free solver tools for higher order compatible finite element discretisation, within the Slate library (previously developed by Thomas Gibson).
Current Team Members
- Hiroe Yamasaki (funded by EPSRC)
- Abdalaziz Hamdan (funded by EPSRC, starting soon)
- Maneesh Kumar Singh (funded by EPSRC)
- Joshua Hope-Collins (funded by UKRI via the Met Office)
- Karina Kowalczyk (funded by EPSRC Roth studentship)
- Thomas Gregory (funded by EPSRC MPECDT, joint-supervised by David Ham)
- Reuben Nixon-Hill (funded by SSCP DTP, joint-supervised by David Ham)
- Sophia Vorderwuelbecke (funded by Roth studentship, joint-supervised by David Ham)
- Lizzie Collingwood (Applied Mathematics MSc)
- Molin Han (UROP [summer intern])
- Kars Knook (UROP [summer intern])
Previous team members
- Werner Bauer was my PDRA from November 2019 until January 2022, and is now a Lecturer at the University of Kingston, shortly to be joining the University of Surrey as a Lecturer.
- Mariana Clare (funded by EPSRC MPECDT, lead supervisor is Matthew Piggott) passed her PhD viva on 14th January 2022.
- Golo Wimmer (funded by EPSRC MPECDT, joint-supervised by Werner Bauer) passed his viva on 29th October 2020.
- Andreas Bock (funded by Roth Studentship), passed his PhD viva on 30th April 2020.
- Thomas Bendall (funded by EPSRC MPECDT), passed his PhD viva on 19th December 2019.
- Jack Betteridge (funded by EPSRC) was my PDRA from October 2019 to April 2020, and has now works with Dr David Ham, still at Imperial College London.
- Thomas Gibson (funded by EPSRC MPECDT, joint-supervised by David Ham) passed his PhD viva on 5th September 2019.
- Jemma Shipton was my PDRA from 2010 until August 2019, and is now a lecturer at the University of Exeter.
- Alastair Gregory (funded by the Science and Solutions for a Changing Planet DTP) passed his viva on 26th March 2018.
- Andrea Natale (funded by Roth Studentship) passed his viva on 22nd August 2017.
- Andrew McRae (jointly supervised with Dr David Ham, funded by Grantham Institute for Climate Change) passed his PhD viva on 27th November 2015.
- Bastien Jordi (jointly supervised with Spencer Sherwin, funded by Marie Curie ANADE programme) passed his PhD viva on 7th October 2015.
- Abeed Visram (funded by EPSRC CASE award with UK Met Office) passed his PhD viva on 18th July 2014.
- Flora MacTavish (funded by Grantham Institute for Climate Change) passed her PhD viva on 19th December 2012.
- Allan Clark (funded by Aeronautics department Doctoral Training Grant) passed his PhD viva on 9th September 2011.