The Mathematical Institute, University of Oxford, Eprints Archive

Multiscale reaction-diffusiion algorithms: PDE-assisted Brownian dynamics

Franz, B. and Flegg, M. B. and Chapman, S. J. and Erban, R. (2013) Multiscale reaction-diffusiion algorithms: PDE-assisted Brownian dynamics. SIAM Journal of Applied Mathematics, 73 (3). pp. 1224-1247.



Two algorithms that combine Brownian dynamics (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.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1783
Deposited By: Sara Jolliffe
Deposited On:14 Feb 2014 08:59
Last Modified:29 May 2015 19:28

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