Simulation of stochastic reaction-diffusion processes on unstructured meshes

Details Simulation of stochastic reaction-diffusion processes on unstructured meshes Simulation of stochastic reaction-diffusion processes on unstructured meshes

2008-04-21

arxiv.org/abs/0804.3288v1

Revised version in SIAM J. Sci. Comput. 31(3):1774-1797, 2009

Mathematics

Numerical Analysis

Scientific paper

10.1137/080721388

Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered by an unstructured mesh and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the Laplace operator on the macroscale. The resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level. The accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology.

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