2012/08/05 by Giorgos Arampatzis, Markos A. Katsoulakis, Arampatzis, Giorgos +3
Materials Science · Mathematics · Physics and Astronomy · #65C05 #65C20 #82C20 #82C26 #Catalytic Processes in Materials Science #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1208.1049
openalex publication_date 2012/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper we study from a numerical analysis perspective the Fractional\nStep Kinetic Monte Carlo (FS-KMC) algorithms proposed in [1] for the parallel\nsimulation of spatially distributed particle systems on a lattice. FS-KMC are\nfractional step algorithms with a time-stepping window \Δ t, and as such\nthey are inherently partially asynchronous since there is no processor\ncommunication during the period \Δ t. In this contribution we primarily\nfocus on the error analysis of FS-KMC algorithms as approximations of\nconventional, serial kinetic Monte Carlo (KMC). A key aspect of our analysis\nrelies on emphasising a goal-oriented approach for suitably defined macroscopic\nobservables (e.g., density, energy, correlations, surface roughness), rather\nthan focusing on strong topology estimates for individual trajectories.\n One of the key implications of our error analysis is that it allows us to\naddress systematically the processor communication of different parallelization\nstrategies for KMC by comparing their (partial) asynchrony, which in turn is\nmeasured by their respective fractional time step \Δ t for a prescribed\nerror tolerance.\n