Accurate Reaction-Diffusion Operator Splitting on Tetrahedral Meshes for Parallel Stochastic Molecular Simulations

TL;DR

This paper presents a novel operator splitting method for reaction-diffusion equations on tetrahedral meshes, enabling scalable parallel stochastic molecular simulations in biology, overcoming serial limitations of exact methods.

Contribution

Introduces an operator splitting approach with improved accuracy for irregular tetrahedral grids, facilitating scalable parallel simulations in molecular biology.

Findings

Demonstrates potential for scalable parallel simulations using MPI

Improves accuracy of reaction-diffusion operator splitting on irregular meshes

Enables larger-scale stochastic molecular simulations in biology

Abstract

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, meaning that the serial limit has already been reached in sub-cellular models. This calls for parallel simulations that can take advantage of the power of modern supercomputers; however exact methods are known to be inherently serial. We introduce an operator splitting implementation for irregular grids with a novel method to improve accuracy, and demonstrate potential for scalable parallel simulations in an initial MPI version. We foresee that this groundwork will enable larger scale, whole-cell stochastic simulations in the near future.