First-Passage Kinetic Monte Carlo method

TL;DR

This paper introduces an efficient, event-driven Monte Carlo method for simulating diffusion-reaction processes by using super-hops and protective domains, significantly improving performance at low particle densities.

Contribution

The paper presents a novel, scalable Monte Carlo algorithm that skips small hops, uses protective domains, and employs first-passage time Green's functions for efficient diffusion-reaction simulations.

Findings

Efficient at low particle densities compared to existing methods.

Reproduces the exact statistics of the underlying model.

Demonstrates significant speed-up in numerical examples.

Abstract

We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the diffusing particles over long distances through a sequence of super-hops, one particle at a time. By partitioning the simulation space into non-overlapping protecting domains each containing only one or two particles, the algorithm factorizes the N-body problem of collisions among multiple Brownian particles into a set of much simpler single-body and two-body problems. Efficient propagation of particles inside their protective domains is enabled through the use of time-dependent Green's functions (propagators) obtained as solutions for the first-passage statistics of random walks. The resulting Monte Carlo algorithm is event-driven and asynchronous; each Brownian particle propagates inside its own protective domain and on its own time clock. The algorithm reproduces the statistics of the underlying Monte-Carlo model exactly. Extensive numerical examples demonstrate that for an important class of diffusion-reaction models the new algorithm is efficient at low particle densities, where other existing algorithms slow down severely.