Imperial College London

DrColinCotter

Faculty of Natural SciencesDepartment of Mathematics

Reader in Numerical Analysis and Scientific Computing
 
 
 
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Contact

 

+44 (0)20 7594 3468colin.cotter

 
 
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Location

 

755Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

76 results found

Cotter CJ, Gottwald GA, 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 AND ENGINEERING SCIENCES, Vol: 473, ISSN: 1364-5021

JOURNAL ARTICLE

Gregory A, Cotter CJ, 2017, On the calibration of multilevel Monte Carlo ensemble forecasts, QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Vol: 143, Pages: 1929-1935, ISSN: 0035-9009

JOURNAL ARTICLE

Natale A, Cotter CJ, 2017, Scale-selective dissipation in energy-conserving finite-element schemes for two-dimensional turbulence, QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Vol: 143, Pages: 1734-1745, ISSN: 0035-9009

JOURNAL ARTICLE

Natale A, Cotter CJ, 2017, A variational $\boldsymbol{H}({\rm div})$ finite-element discretization approach for perfect incompressible fluids, IMA Journal of Numerical Analysis, ISSN: 0272-4979

JOURNAL ARTICLE

Yamazaki H, Shipton J, Cullen MJP, Mitchell L, Cotter CJet al., 2017, Vertical slice modelling of nonlinear Eady waves using a compatible finite element method, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 343, Pages: 130-149, ISSN: 0021-9991

JOURNAL ARTICLE

Abolghasemi MA, Piggott MD, Spinneken J, Vire A, Cotter CJ, Crammond Set al., 2016, Simulating tidal turbines with multi-scale mesh optimisation techniques, JOURNAL OF FLUIDS AND STRUCTURES, Vol: 66, Pages: 69-90, ISSN: 0889-9746

JOURNAL ARTICLE

Cotter CJ, Eldering J, Holm DD, Jacobs HO, Meier DMet al., 2016, Weak dual pairs and jetlet methods for ideal incompressible fluid models in n >= 2 dimensions, Journal of Nonlinear Science, Vol: 26, Pages: 1723-1765, ISSN: 1432-1467

We review the role of dual pairs in mechanics and use them to derive particle-like solutions to regularized incompressible fluid systems. In our case we have a dual pair resulting from the action of diffeomorphisms on point particles (essentially by moving the points). We then augment our dual pair by considering the action of diffeomorphisms on Taylor series, also known as jets. The augmented weak dual pairs induce a hierarchy of particle-like solutions and conservation laws with particles carrying a copy of a jet group. We call these augmented particles jetlets. The jet groups serve as finite-dimensional models of the diffeomorphism group itself, and so the jetlet particles serve as a finite-dimensional model of the self-similarity exhibited by ideal incompressible fluids. The conservation law associated to jetlet solutions is shown to be a shadow of Kelvin’s circulation theorem. Finally, we study the dynamics of infinite time particle mergers. We prove that two merging particles at the zeroth level in the hierarchy yield dynamics which asymptotically approach that of a single particle in the first level in the hierarchy. This merging behavior is then verified numerically as well as the exchange of angular momentum which must occur during a near collision of two particles. The resulting particle-like solutions suggest a new class of meshless methods which work in dimensions n≥2n≥2 and which exhibit a shadow of Kelvin’s circulation theorem. More broadly, this provides one of the first finite-dimensional models of self-similarity in ideal fluids.

JOURNAL ARTICLE

Cotter CJ, Kirby RC, 2016, Mixed finite elements for global tide models, NUMERISCHE MATHEMATIK, Vol: 133, Pages: 255-277, ISSN: 0029-599X

JOURNAL ARTICLE

Cotter CJ, Kuzmin D, 2016, Embedded discontinuous Galerkin transport schemes with localised limiters, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 311, Pages: 363-373, ISSN: 0021-9991

JOURNAL ARTICLE

Gregory A, Cotter CJ, Reich S, 2016, MULTILEVEL ENSEMBLE TRANSFORM PARTICLE FILTERING, SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol: 38, Pages: A1317-A1338, ISSN: 1064-8275

JOURNAL ARTICLE

Mcrae ATT, Bercea G-T, Mitchell L, Ham DA, Cotter CJet al., 2016, AUTOMATED GENERATION AND SYMBOLIC MANIPULATION OF TENSOR PRODUCT FINITE ELEMENTS, SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol: 38, Pages: S25-S47, ISSN: 1064-8275

JOURNAL ARTICLE

Natale A, Shipton J, Cotter CJ, 2016, Compatible finite element spaces for geophysical fluid dynamics, Dynamics and Statistics of the Climate System, Vol: 1

JOURNAL ARTICLE

Jordi BE, Cotter CJ, Sherwin SJ, 2015, An adaptive selective frequency damping method, PHYSICS OF FLUIDS, Vol: 27, ISSN: 1070-6631

JOURNAL ARTICLE

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, Publisher: Cambridge University Press, ISBN: 9781107663916

BOOK

Thuburn J, Cotter CJ, 2015, A primal-dual mimetic finite element scheme for the rotating shallow water equations on polygonal spherical meshes, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 290, Pages: 274-297, ISSN: 0021-9991

JOURNAL ARTICLE

Cotter CJ, Holm DD, 2014, Variational formulations of sound-proof models, Quarterly Journal of the Royal Meteorological Society

JOURNAL ARTICLE

Cotter CJ, Holm DD, Jacobs HO, Meier DMet al., 2014, A jetlet hierarchy for ideal fluid dynamics, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 47, ISSN: 1751-8113

JOURNAL ARTICLE

Cotter CJ, McRae ATT, 2014, Compatible finite element methods for numerical weather prediction

This article takes the form of a tutorial on the use of a particular class ofmixed finite element methods, which can be thought of as the finite elementextension of the C-grid staggered finite difference method. The class is oftenreferred to as compatible finite elements, mimetic finite elements, discretedifferential forms or finite element exterior calculus. We provide anelementary introduction in the case of the one-dimensional wave equation,before summarising recent results in applications to the rotating shallow waterequations on the sphere, before taking an outlook towards applications inthree-dimensional compressible dynamical cores.

JOURNAL ARTICLE

Cotter CJ, McRae ATT, 2014, Compatible finite elements for numerical weather prediction, ECMWF Annual Seminar

CONFERENCE PAPER

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, ISSN: 0021-9991

JOURNAL ARTICLE

Farrell PE, Cotter CJ, Funke SW, 2014, A framework for the automation of generalised stability theory, SIAM Journal on Scientific Computing, Vol: 36, Pages: C25-C48

JOURNAL ARTICLE

Jordi BE, Cotter CJ, Sherwin SJ, 2014, Encapsulated formulation of the selective frequency damping method, PHYSICS OF FLUIDS, Vol: 26, ISSN: 1070-6631

JOURNAL ARTICLE

McRae ATT, Cotter CJ, 2014, Energy- and enstrophy-conserving schemes for the shallow-water equations, based on mimetic finite elements, Quarterly Journal of the Royal Meteorological Society

This paper presents a family of spatial discretisations of the nonlinearrotating shallow-water equations that conserve both energy and potentialenstrophy. These are based on two-dimensional mixed finite element methods, andhence, unlike some finite difference methods, do not require an orthogonalgrid. Numerical verification of the aforementioned properties is also provided.

JOURNAL ARTICLE

Melvin T, Staniforth A, Cotter C, 2014, A two-dimensional mixed finite-element pair on rectangles, Quarterly Journal of the Royal Meteorological Society, Vol: 140, Pages: 930-942, ISSN: 0035-9009

JOURNAL ARTICLE

Thuburn J, Cotter CJ, Dubos T, 2014, A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids, Geoscientific Model Development, Vol: 7, Pages: 909-929

JOURNAL ARTICLE

Visram AR, Cotter CJ, Cullen MJP, 2014, A framework for evaluating model error using asymptotic convergence in the Eady model, Quarterly Journal of the Royal Meteorological Society, Pages: n/a-n/a, ISSN: 0035-9009

JOURNAL ARTICLE

Cotter C, 2013, Data assimilation on the exponentially accurate slow manifold, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 371, ISSN: 1364-503X

JOURNAL ARTICLE

Cotter CJ, Cotter SL, Vialard F-X, 2013, Bayesian data assimilation in shape registration, INVERSE PROBLEMS, Vol: 29, ISSN: 0266-5611

JOURNAL ARTICLE

Cotter CJ, Holm DD, 2013, On Noether's Theorem for the Euler-Poincar, Equation on the Diffeomorphism Group with Advected Quantities, FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, Vol: 13, Pages: 457-477, ISSN: 1615-3375

JOURNAL ARTICLE

Cotter CJ, Holm DD, 2013, A variational formulation of vertical slice models, Proc. R. Soc. A, Vol: 469

JOURNAL ARTICLE

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