Simulation of stochastic reaction-diffusion processes on unstructured meshes
Abstract
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.
Cite
@article{arxiv.0804.3288,
title = {Simulation of stochastic reaction-diffusion processes on unstructured meshes},
author = {Stefan Engblom and Lars Ferm and Andreas Hellander and Per Lötstedt},
journal= {arXiv preprint arXiv:0804.3288},
year = {2009}
}