Parallelization, Processor Communication and Error Analysis in Lattice Kinetic Monte Carlo

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 windowt, and as such they are inherently partially asynchronous since there is no processor com- munication during the periodt. 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 as- pect of our analysis relies on emphasizing 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 stept for a prescribed error tolerance.

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