Simulation of stochastic reaction-diffusion processes on unstructured meshes

TL;DR

This paper presents a flexible hybrid simulation method for stochastic reaction-diffusion systems on unstructured meshes, combining mesoscopic and macroscopic approaches, with demonstrated accuracy in biological applications.

Contribution

It introduces a novel hybrid algorithm that integrates mesoscopic and macroscopic modeling of stochastic reaction-diffusion processes on unstructured meshes.

Findings

The method accurately simulates reaction-diffusion systems in biological contexts.

It offers computational efficiency through hybrid meso-macro modeling.

Numerical examples validate the approach's effectiveness.

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.