Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes

  • Authors:

  • Stefan Engblom;Lars Ferm;Andreas Hellander;Per Lötstedt

  • Affiliations:

  • stefane@it.uu.se and ferm@it.uu.se and andreas.hellander@it.uu.se and perl@it.uu.se;-;-;-

  • Venue:
  • SIAM Journal on Scientific Computing
  • Year:
  • 2009

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Abstract

We model stochastic chemical systems with diffusion by 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 a discretized Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered in our method 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.