Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Professor of Computational Mathematics



+44 (0)20 7594 3468colin.cotter




755Huxley BuildingSouth Kensington Campus





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.

Current Team Members

Research Associates:

  • Werner Bauer (funded by NERC)
  • Hiroe Yamasaki (funded by EPSRC)

PhD students:

  • 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)
  • Mariana Clare (funded by EPSRC MPECDT, lead supervisor is Matthew Piggott)

Previous team members:

  • 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

Recent and future seminars and conferences

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  • ECFD 2018, Glasgow (invited talk), 11-15 June 2017
  • DWD Seminar, Offenbach. 4 Dec 2017
  • Mathematical Geosciences seminar, Mathematical Institute, Oxford. 3 Nov 2017
  • Workshop on Classic and Stochastic Approaches to Mathematical Fluid Dynamics, Imperial College London (workshop co-organiser), 2-6 Oct 2017
  • SciCADE 17, University of Bath (invited talk), 11-15 Sept 2017.
  • Forschungsseminar Geophysical Fluid Dynamics, Freien Universität Berlin, 12 July 2017
  • Workshop on New Trends in Applied Geometric Mechanics, ICMAT, Madrid. 3-7 Jul 2017
  • Workshop on Geometric Methods for Geophysical Fluid Dynamics, Hamburg (invited talk), 5-7 June 2017
  • British Applied Mathematics Colloquium 2017, University of Surrey (invited talk), 10-12 Apr 2017
  • Firedrake '17, Imperial College London (contributed talk), 27-28 Mar 2017
  • Mathematics of Planet Earth Centre for Doctoral Training Jamboree 2017, Imperial College London (co-organiser), 20-22 Mar 2017
  • SIAM Computational Science and Engineering 2017, Atlanta (minisymposium convenor), 27 Feb - 3 Mar 2017
  • Workshop on Numerical Methods for Geophysical Fluid Dynamics, Imperial College London (organiser), 13-14 Feb 2017
  • Oberwolfach Seminar: Mathematical and Algorithmic Aspects of Data Assimilation in the Geosciences, (invited talk), 2-8 Oct 2016
  • Maths Foresees General Assembly, Edinburgh, (co-organiser) 5-7 Sept 2016
  • Gung-Ho Plenary, STFC Daresbury, (presenter) 12-13 July 2016
  • Moving Mesh Adaptivity workshop, Bath (organising committee and contributed talk), 13-15 June 2016
  • DG Methods and Finite Element Software, Bath (invited talk), 30 May - 1 June 2016
  • FENICS 2016, Oslo (contributed talk), 18-20 May 2016
  • Numerical Analysis Seminar, University of Manchester, 13 May 2016
  • Multiscale Modeling and its Applications - From Weather and Climate Models to Models of Materials Defects, Fields Institute, Toronto (plenary talk) 20-22 April 2016
  • EMCWF Workshop on Model Uncertainty (workshop participant), 11-15 April, 2016
  • High-Dimensional Statistical Models & Big Data: Methodology & Applications, Alan Turing Institute, London (invited talk), 10 - 12 February 2016
  • Gung Ho conference, Met Office, Exeter (invited talk), 2 - 6 November 2015
  • Maths Foresees Study Group, Cambridge (organising committee), 21-24 September 2015
  • Climathnet 2015 conference, Bath (organising committee and contributed talk), 6-10 July 2015
  • FENICS 2015, Imperial College London (local organising committee and contributed talk), 29 June - 1 July 2015
  • Maths Foresees workshop, Leeds (network management team), 18-20 May 2015
  • ICMS Galerkin methods with applications in weather and climate workshop, Edinburgh, (workshop organiser and contributed talk), 23-27 March 2015
  • SIAM CSE 2015, Salt Lake City (invited minisymposium talk), 14-18 March 2015
  • GungHo Plenary, Bath, (presenter) 3-4 November 2014
  • WCCM XI, Barcelona (invited minisymposium talk), 20-25 July 2014
  • FeNICS '14, University of Chicago @ Paris (contributed talk), 16-17 June 2014
  • Shape 2014, Imperial College London (invited talk), 10-13 June 2014
  • AGM Meeting on Geometric Fluid Dynamics, University of Surrey (invited talk), 16 May 2014
  • Computational Mathematics and Applications seminar, University of Oxford, 22 May 2014
  • Modelisation Mathematique et Calcul Scientifique seminar, Lyon 1, 13 May 2014
  • Fluids Seminar, Civil Engineering, Imperial College London, 28 April 2014
  • GungHo Plenary, (presenter) 30/31st April 2014
  • ECMWF Scalabiilty Workshop, 14-15 April 2014
  • PDEs on the Sphere 2014, Boulder (contributed talk), 7-11 April 2014
  • Mathematics of the Fluid Earth, London Mathematical Society (invited speaker), 5-7 February 2014
  • SIAM PDEs 2013, Orlando (invited minisymposium talk), 7-10 December 2013
  • GungHo Plenary, Reading, (presenter) 2/3 December 2013
  • Applied Mathematics Seminar, Warwick, 8 November 2013
  • Grantham Institute workshop on Numerical Methods for Geophysical Fluid Dynamics, Imperial College London (workshop organiser), 8-9 October 2013
  • SciCADE 2013, Valladolid (Structure-Preserving Numerical Methods minisymposium organiser), 16-20 September 2013
  • Challenger Society for Marine Science Ocean Modelling meeting, Imperial College London (invited speaker), 9-10 September 2013
  • ECMWF Annual Seminar (invited speaker), 2-6 September 2013
  • GungHo Plenary, (presenter) University of Manchester, 30/31 July 2013
  • SIAM Geosciences, Padova (invited minisymposium talk), 17-20 June 2013
  • GungHo Plenary, (presenter) University of Exeter, 18-19 April 2013
  • FeNICS '13 at University of Cambridge (contributed talk), 18-19 March 2013
  • Applied Mathematics Seminar, University of Edinburgh, 28 February 2013
  • Applied Mathematics Seminar, Leeds, 28 January 2013
  • Isaac Institute programme on Multiscale Numerics for the Atmosphere and Ocean (programme fellow), December 2012

Other Stuff

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