Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics

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

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

Abstract

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
Volume73
Issue number3
DOIs
StatePublished - Jun 19 2013
Externally publishedYes

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