Giorgos Arampatzis, Markos A. Katsoulakis, Petr Plechac
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 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 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 step $\Delta t$ for a prescribed error tolerance.
Bibliographical note:
submitted to SIAM J. Numer. Anal.
preprint on arXiv:
Department of Mathematical 