Temporal acceleration of spatially distributed kinetic Monte Carlo simulations

The computational intensity of kinetic Monte Carlo (KMC) simulation is a major impediment in simulating large length and time scales. In recent work, an approximate method for KMC simulation of spatially uniform systems, termed the binomial τ-leap method, was introduced [A. Chatterjee, D.G. Vlachos, M.A. Katsoulakis, Binomial distribution based τ-leap accelerated stochastic simulation, J. Chem. Phys. 122 (2005) 024112], where molecular bundles instead of individual processes are executed over coarse-grained time increments. This temporal coarse-graining can lead to significant computational savings but its generalization to spatially lattice KMC simulation has not been realized yet. Here we extend the binomial τ-leap method to lattice KMC simulations by combining it with spatially adaptive coarse-graining. Absolute stability and computational speed-up analyses for spatial systems along with simulations provide insights into the conditions where accuracy and substantial acceleration of the new spatio-temporal coarse-graining method are ensured. Model systems demonstrate that the r-time increment criterion of Chatterjee et al. obeys the absolute stability limit for values of r up to near 1.