@TechReport{ it:2008-012,
author = {Stefan Engblom and Lars Ferm and Andreas Hellander and Per
L{\"o}tstedt},
title = {Simulation of Stochastic Reaction-Diffusion Processes on
Unstructured Meshes},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2008},
number = {2008-012},
month = apr,
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.}
}