Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

Handle URI:
http://hdl.handle.net/10754/597453
Title:
Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
Authors:
Cotter, Simon L.; Vejchodský, Tomáš; Erban, Radek
Abstract:
Stochastic 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.
Citation:
Cotter 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.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2013
DOI:
10.1137/120877374
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
Submitted 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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorCotter, Simon L.en
dc.contributor.authorVejchodský, Tomášen
dc.contributor.authorErban, Radeken
dc.date.accessioned2016-02-25T12:33:32Zen
dc.date.available2016-02-25T12:33:32Zen
dc.date.issued2013-01en
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.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/120877374en
dc.identifier.urihttp://hdl.handle.net/10754/597453en
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.en
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.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAdaptive meshesen
dc.subjectChemical Fokker-Plancken
dc.subjectFinite element methodsen
dc.subjectStochastic simulation algorithmen
dc.titleAdaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systemsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversity of Manchester, Manchester, United Kingdomen
dc.contributor.institutionAcademy of Sciences of the Czech Republic, Prague, Czech Republicen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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