Analysis of the two-regime method on square meshes

TL;DR

This paper extends the two-regime method (TRM) for stochastic reaction-diffusion simulations from one-dimensional models to higher dimensions, specifically focusing on square meshes and the coupling of Brownian dynamics with compartment-based models in 2D.

Contribution

The paper generalizes the TRM to two-dimensional square meshes, analyzing interface geometries including flat parts and corners, and discusses parameter choices for effective coupling.

Findings

TRM is successfully extended to 2D square meshes.

Theoretical analysis supports the use of 1D theory along interface normals.

Parameter choices depend on compartment size and time step.

Abstract

The two-regime method (TRM) has been recently developed for optimizing stochastic reaction-diffusion simulations. It is a multiscale (hybrid) algorithm which uses stochastic reaction-diffusion models with different levels of detail in different parts of the computational domain. The coupling condition on the interface between different modelling regimes of the TRM was previously derived for one-dimensional models. In this paper, the TRM is generalized to higher dimensional reaction-diffusion systems. Coupling Brownian dynamics models with compartment-based models on regular (square) two-dimensional lattices is studied in detail. In this case, the interface between different modelling regimes contain either flat parts or right-angled corners. Both cases are studied in the paper. For flat interfaces, it is shown that the one-dimensional theory can be used along the line perpendicular to the TRM interface. In the direction tangential to the interface, two choices of the TRM parameters are presented. Their applicability depends on the compartment size and the time step used in the molecular-based regime. The two-dimensional generalization of the TRM is also discussed in the case of corners.