Franz, B. and Flegg, M. B. and Chapman, S. J. and Erban, R.
Multiscale reaction-diffusion algorithms: pde-assisted
Brownian dynamics. SIAM Journal on Applied Mathematics . (Submitted)
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 to accurately compute variances using the PBD simulation requires the overlap region. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented.
|Subjects:||D - G > General|
|Research Groups:||Oxford Centre for Collaborative Applied Mathematics|
|Deposited By:||Peter Hudston|
|Deposited On:||20 Jul 2012 06:56|
|Last Modified:||29 May 2015 19:15|
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