Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 73, Issue 3, Pages 1224-1247Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120882469
Keywords
reaction-diffusion systems; Brownian dynamics; multiscale simulation
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Funding
- European Research Council under the European Community's Seventh Framework Programme (FP7)/ERC [239870]
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04]
- Royal Society University Research Fellowship
- Nicholas Kurti Junior Fellowship of Brasenose College, University of Oxford
- Philip Leverhulme Prize
- Leverhulme Trust
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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.
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