# ProfessorColinCotter

Faculty of Natural SciencesDepartment of Mathematics

Professor of Computational Mathematics

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### Contact

+44 (0)20 7594 3468colin.cotter

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### Location

755Huxley BuildingSouth Kensington Campus

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# Citation

## BibTex format

@unpublished{Cotter:2019,author = {Cotter, C and Crisan, D and Holm, DD and Pan, W and Shevchenko, I},publisher = {arXiv},title = {A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation},url = {http://arxiv.org/abs/1907.11884v1},year = {2019}}

## RIS format (EndNote, RefMan)

TY  - UNPBAB  - In this work, we apply a particle filter with three additional procedures(model reduction, tempering and jittering) to a damped and forcedincompressible 2D Euler dynamics defined on a simply connected bounded domain.We show that using the combined algorithm, we are able to successfullyassimilate data from a reference system state (the truth") modelled by ahighly resolved numerical solution of the flow that has roughly $3.1\times10^6$degrees of freedom for $10$ eddy turnover times, using modest computationalhardware.  The model reduction is performed through the introduction of a stochasticadvection by Lie transport (SALT) model as the signal on a coarser resolution.The SALT approach was introduced as a general theory using a geometricmechanics framework from Holm, Proc. Roy. Soc. A (2015). This work follows onthe numerical implementation for SALT presented by Cotter et al, SIAMMultiscale Model. Sim. (2019) for the flow in consideration. The modelreduction is substantial: The reduced SALT model has $4.9\times 10^4$ degreesof freedom.  Forecast reliability and estimated asymptotic behaviour of the particlefilter are also presented.AU  - Cotter,CAU  - Crisan,DAU  - Holm,DDAU  - Pan,WAU  - Shevchenko,IPB  - arXivPY  - 2019///TI  - A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equationUR  - http://arxiv.org/abs/1907.11884v1UR  - http://hdl.handle.net/10044/1/72321ER  -