Uppsala University Department of Information Technology

Technical Report 2008-012

Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes

Stefan Engblom, Lars Ferm, Andreas Hellander, and Per Lötstedt

April 2008

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.

Available as PDF (483 kB, no cover)

Download BibTeX entry.



Uppsala Universitet