Efficient Monte Carlo methods for simulating diffusion-reaction processes in complex systems

TL;DR

This paper reviews fast random walk algorithms, a Monte Carlo method that efficiently simulates diffusion-reaction processes in complex, heterogeneous systems, enabling detailed probabilistic analysis and PDE solutions.

Contribution

It introduces the principles and applications of FRW algorithms, highlighting their adaptability and efficiency in complex media for simulating diffusion-reaction phenomena.

Findings

FRW algorithms effectively simulate diffusive trajectories in complex media.

They accurately compute probabilistic characteristics like reaction rates and exit times.

FRWs are versatile for solving related PDEs in irregular geometries.

Abstract

We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to study various probabilistic characteristics (harmonic measure, first passage/exit time distribution, reaction rates, search times and strategies, etc.) and to solve the related partial differential equations. The adaptive character and flexibility of FRWs make them particularly efficient for simulating diffusive processes in porous, multiscale, heterogeneous, disordered or irregularly-shaped media.