Parallelization, processor communication and error analysis in lattice kinetic Monte Carlo

TL;DR

This paper analyzes the error and communication efficiency of Fractional Step Kinetic Monte Carlo algorithms for parallel lattice particle simulations, emphasizing a goal-oriented approach for macroscopic observables.

Contribution

It provides a systematic error analysis of FS-KMC algorithms focusing on macroscopic observables and compares different parallelization strategies based on their asynchrony.

Findings

Error bounds for FS-KMC algorithms are derived.

A goal-oriented approach improves the analysis of macroscopic observables.

Parallelization strategies are compared through their fractional time step and error tolerance.

Abstract

In this paper we study from a numerical analysis perspective the Fractional Step Kinetic Monte Carlo (FS-KMC) algorithms proposed in [1] for the parallel simulation of spatially distributed particle systems on a lattice. FS-KMC are fractional step algorithms with a time-stepping window $\Delta t$, and as such they are inherently partially asynchronous since there is no processor communication during the period $\Delta t$. In this contribution we primarily focus on the error analysis of FS-KMC algorithms as approximations of conventional, serial kinetic Monte Carlo (KMC). A key aspect of our analysis relies on emphasising a goal-oriented approach for suitably defined macroscopic observables (e.g., density, energy, correlations, surface roughness), rather than focusing on strong topology estimates for individual trajectories. One of the key implications of our error analysis is that it allows us to address systematically the processor communication of different parallelization strategies for KMC by comparing their (partial) asynchrony, which in turn is measured by their respective fractional time step $\Delta t$ for a prescribed error tolerance.