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dc.contributor.authorCotter, Simon L.
dc.contributor.authorVejchodský, Tomáš
dc.contributor.authorErban, Radek
dc.date.accessioned2016-02-25T12:33:32Z
dc.date.available2016-02-25T12:33:32Z
dc.date.issued2013-01
dc.identifier.citationCotter SL, Vejchodský T, Erban R (2013) Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems. SIAM Journal on Scientific Computing 35: B107–B131. Available: http://dx.doi.org/10.1137/120877374.
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/120877374
dc.identifier.urihttp://hdl.handle.net/10754/597453
dc.description.abstractStochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods. © 2013 Society for Industrial and Applied Mathematics.
dc.description.sponsorshipSubmitted to the journal's Computational Methods in Science and Engineering section May 15, 2012; accepted for publication (in revised form) December 3, 2012; published electronically January 10, 2013. This work was supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 239870 and was based on work supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom (simon.cotter@manchester.ac.uk). This author's work was partially supported by a Junior Research Fellowship of St Cross College, University of Oxford.Institute of Mathematics, Czech Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic (vejchod@math.cas.cz). This author's work was supported by the Grant Agency of the Academy of Sciences (project IAA100190803) and RVO 67985840.Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, United Kingdom (erban@maths.ox.ac.uk). This author's work was supported by Somerville College, University of Oxford, by a Fulford Junior Research Fellowship; Brasenose College, University of Oxford, by a Nicholas Kurti Junior Fellowship; the Royal Society for a University Research Fellowship; and the Leverhulme Trust for a Philip Leverhulme Prize. This prize money was used to support research visits of Tomas Vejchodsky in Oxford.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectAdaptive meshes
dc.subjectChemical Fokker-Planck
dc.subjectFinite element methods
dc.subjectStochastic simulation algorithm
dc.titleAdaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
dc.typeArticle
dc.identifier.journalSIAM Journal on Scientific Computing
dc.contributor.institutionUniversity of Manchester, Manchester, United Kingdom
dc.contributor.institutionAcademy of Sciences of the Czech Republic, Prague, Czech Republic
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
kaust.grant.numberKUK-C1-013-04


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