Summary
My research in numerical analysis and scientific computing focusses on the design, analysis and implementation of numerical methods for weather forecasting, ocean modelling and climate simulation. Recently, I have been developing compatible finite element methods and time parallel algorithms for these applications. I am motivated by the geometric variational structure of fluid equations, which are also relevant for algorithms for exploring the geometric structure of shapes and images. I also develop numerical algorithms for probabilistic forecasting and data assimilation, and am currently developing particle filters for stochastic partial differential equations.
I am co-Director for the Mathematics of Planet Earth Centre for Doctoral Training, and a co-Investigator for the Platform for Research in Simulation Methods. I am also an Associate Editor for Foundations of Data Science (was previously Associate Editor for for the Quarterly Journal of the Royal Meteorological Society) and am a member of the EPSRC peer review college. I wrote a book with Sebastian Reich, entitled "Probabilistic Forecasting and Bayesian Data Assimliation".
See my research page for the list of current and past PhD and postdoctoral researchers.
Biography
- Professor of Computational Mathematics, Department of Mathematics, Imperial College London, July 2019 - date
- Reader in Numerical Analysis and Scientific Computing, Department of Mathematics, Imperial College London, July 2016 - July 2019
- Senior Lecturer in the Department of Mathematics, Imperial College London, November 2013 to July 2016
- Senior Lecturer in the Department of Aeronautics, Imperial College London 2010-2013
- Lecturer in the Department of Aeronautics, Imperial College London 2006-2010
- Postdoctoral researcher in the Department of Mathematics, Imperial College London 2005-2006
- Postdoctoral researcher in the Department of Earth Science and Engineering, Imperial College London 2004-2005
- PhD Mathematics, Imperial College London 2000-2004
- Part III, Mathematics, Fitzwilliam College, Cambridge University 1999-2000
- BA Mathematics, Fitzwilliam College, Cambridge University 1996-1999
My Google Scholar profile is here. Preprints of many of my papers can be found here.
Selected Publications
Journal Articles
Cotter CJ, Deasy J, Pryer T, 2020, The r-Hunter-Saxton equation, smooth and singular solutions and their approximation, Nonlinearity, Vol:33, ISSN:0951-7715, Pages:7016-7039
Wimmer GA, Cotter CJ, Bauer W, 2020, Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations, Journal of Computational Physics, Vol:401, ISSN:0021-9991, Pages:1-18
Cotter CJ, Crisan D, Holm DD, et al., 2019, Numerically modelling stochastic lie transport in fluid dynamics, SIAM Journal on Scientific Computing, Vol:17, ISSN:1064-8275, Pages:192-232
Cotter CJ, Graber PJ, Kirby RC, 2018, Mixed finite elements for global tide models with nonlinear damping, Numerische Mathematik, Vol:140, ISSN:0029-599X, Pages:963-991
Gregory ACA, Cotter CJ, 2017, A seamless multilevel ensemble transform particle filter, Siam Journal on Scientific Computing, Vol:39, ISSN:1095-7197, Pages:A2684-A2701
Cotter CJ, Gottwald G, Holm DD, 2017, Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol:473, ISSN:1364-5021
Natale A, Cotter CJ, 2017, A variational H (div) finite-element discretization approach for perfect incompressible fluids, IMA Journal of Numerical Analysis, Vol:38, ISSN:0272-4979, Pages:1388-1419
Natale A, Shipton J, Cotter CJ, 2016, Compatible finite element spaces for geophysical fluid dynamics, Dynamics and Statistics of the Climate System, Vol:1, ISSN:2059-6987
Cotter CJ, Thuburn J, 2014, A finite element exterior calculus framework for the rotating shallow-water equations, Journal of Computational Physics, Vol:257, Pages:1506-1526
Cotter CJ, Shipton J, 2012, Mixed finite elements for numerical weather prediction, J. Comp. Phys.
Books
Reich S, Cotter CJ, 2015, Probabilistic Forecasting and Bayesian Data Assimilation, http://www.cambridge.org/us/academic/subjects/mathematics/computational-science/probabilistic-forecasting-and-bayesian-data-assimilation, Cambridge University Press, ISBN:9781107663916