Handle URI:
http://hdl.handle.net/10754/597565
Title:
Analysis of the Two-Regime Method on Square Meshes
Authors:
Flegg, Mark B.; Chapman, S. Jonathan; Zheng, Likun; Erban, Radek
Abstract:
The two-regime method (TRM) has been recently developed for optimizing stochastic reaction-diffusion simulations [M. Flegg, J. Chapman, and R. Erban, J. Roy. Soc. Interface, 9 (2012), pp. 859-868]. It is a multiscale (hybrid) algorithm which uses stochastic reaction-diffusion models with different levels of detail in different parts of the computational domain. The coupling condition on the interface between different modeling regimes of the TRM was previously derived for onedimensional models. In this paper, the TRM is generalized to higher dimensional reaction-diffusion systems. Coupling Brownian dynamics models with compartment-based models on regular (square) two-dimensional lattices is studied in detail. In this case, the interface between different modeling regimes contains either flat parts or right-angle corners. Both cases are studied in the paper. For flat interfaces, it is shown that the one-dimensional theory can be used along the line perpendicular to the TRM interface. In the direction tangential to the interface, two choices of the TRM parameters are presented. Their applicability depends on the compartment size and the time step used in the molecular-based regime. The two-dimensional generalization of the TRM is also discussed in the case of corners. © 2014 Society for Industrial and Applied Mathematics.
Citation:
Flegg MB, Chapman SJ, Zheng L, Erban R (2014) Analysis of the Two-Regime Method on Square Meshes. SIAM Journal on Scientific Computing 36: B561–B588. Available: http://dx.doi.org/10.1137/130915844.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2014
DOI:
10.1137/130915844
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This work was supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. 239870 and in part by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).The fourth author's work was also supported by a Royal Society University Research Fellowship; by a Nicholas Kurti Junior Fellowship from Brasenose College, University of Oxford; and by the Philip Leverhulme Prize from the Leverhulme Trust.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorFlegg, Mark B.en
dc.contributor.authorChapman, S. Jonathanen
dc.contributor.authorZheng, Likunen
dc.contributor.authorErban, Radeken
dc.date.accessioned2016-02-25T12:42:10Zen
dc.date.available2016-02-25T12:42:10Zen
dc.date.issued2014-01en
dc.identifier.citationFlegg MB, Chapman SJ, Zheng L, Erban R (2014) Analysis of the Two-Regime Method on Square Meshes. SIAM Journal on Scientific Computing 36: B561–B588. Available: http://dx.doi.org/10.1137/130915844.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/130915844en
dc.identifier.urihttp://hdl.handle.net/10754/597565en
dc.description.abstractThe two-regime method (TRM) has been recently developed for optimizing stochastic reaction-diffusion simulations [M. Flegg, J. Chapman, and R. Erban, J. Roy. Soc. Interface, 9 (2012), pp. 859-868]. It is a multiscale (hybrid) algorithm which uses stochastic reaction-diffusion models with different levels of detail in different parts of the computational domain. The coupling condition on the interface between different modeling regimes of the TRM was previously derived for onedimensional models. In this paper, the TRM is generalized to higher dimensional reaction-diffusion systems. Coupling Brownian dynamics models with compartment-based models on regular (square) two-dimensional lattices is studied in detail. In this case, the interface between different modeling regimes contains either flat parts or right-angle corners. Both cases are studied in the paper. For flat interfaces, it is shown that the one-dimensional theory can be used along the line perpendicular to the TRM interface. In the direction tangential to the interface, two choices of the TRM parameters are presented. Their applicability depends on the compartment size and the time step used in the molecular-based regime. The two-dimensional generalization of the TRM is also discussed in the case of corners. © 2014 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis work was supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. 239870 and in part by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).The fourth author's work was also supported by a Royal Society University Research Fellowship; by a Nicholas Kurti Junior Fellowship from Brasenose College, University of Oxford; and by the Philip Leverhulme Prize from the Leverhulme Trust.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectMultiscale modelingen
dc.subjectStochastic reaction-diffusion simulationsen
dc.subjectTwo-regime methoden
dc.titleAnalysis of the Two-Regime Method on Square Meshesen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUC Irvine, Irvine, United Statesen
kaust.grant.numberKUK-C1-013-04en
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