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

摘要

In this paper we study from a numerical analysis perspective the FractionalStep Kinetic Monte Carlo (FS-KMC) algorithms proposed in [1] for the parallelsimulation of spatially distributed particle systems on a lattice. FS-KMC arefractional step algorithms with a time-stepping window $\Delta t$, and as suchthey are inherently partially asynchronous since there is no processorcommunication during the period $\Delta t$. In this contribution we primarilyfocus on the error analysis of FS-KMC algorithms as approximations ofconventional, serial kinetic Monte Carlo (KMC). A key aspect of our analysisrelies on emphasising a goal-oriented approach for suitably defined macroscopicobservables (e.g., density, energy, correlations, surface roughness), ratherthan focusing on strong topology estimates for individual trajectories. One of the key implications of our error analysis is that it allows us toaddress systematically the processor communication of different parallelizationstrategies for KMC by comparing their (partial) asynchrony, which in turn ismeasured by their respective fractional time step $\Delta t$ for a prescribederror tolerance.