Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics

Benjamin Franz, Mark B. Flegg, S. Jonathan Chapman, Radek Erban

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)1224-1247
Number of pages24
JournalSIAM Journal on Applied Mathematics
Issue number3
StatePublished - Jun 19 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: Received by the editors June 26, 2012; accepted for publication (in revised form) March 6, 2013; published electronically June 19, 2013. The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 239870. This publication was based on work supported in part by Award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).Corresponding author. Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK ( This author's work was supported by a Royal Society University Research Fellowship; by a Nicholas Kurti Junior Fellowship of Brasenose College, University of Oxford; and by a Philip Leverhulme Prize awarded by the Leverhulme Trust.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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