Generating discrete random variables in a computer
Communications of the ACM
Splitting for rare event simulation in biochemical systems
Proceedings of the 6th International ICST Conference on Simulation Tools and Techniques
Monte-carlo simulation of the oscillatory dynamics of a catalytic reaction with lateral interactions
Computational Mathematics and Modeling
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This paper concerns kinetic Monte Carlo (KMC) algorithms that have a single-event execution time independent of the system size. Two methods are presented-one that combines the use of inverted-list data structures with rejection Monte Carlo and a second that combines inverted lists with the Marsaglia-Norman-Cannon algorithm. The resulting algorithms apply to models with rates that are determined by the local environment but are otherwise arbitrary, time-dependent and spatially heterogeneous. While especially useful for crystal growth simulation, the algorithms are presented from the point of view that KMC is the numerical task of simulating a single realization of a Markov process, allowing application to a broad range of areas where heterogeneous random walks are the dominate simulation cost.