An accelerated kinetic Monte Carlo simulation algorithm was presented for studying molecular beam epitaxial growth during step flow. The acceleration was achieved by allowing adatoms far from the step edges to execute larger jumps with correspondingly reduced rates. The computational complexities of a number of different algorithmic implementations were analyzed and compared. The scaling of the accelerated algorithms were verified by test runs performed on a one-dimensional model. Both performance and accuracy were evaluated. One to two orders of magnitude increases of efficiency were achieved while preserving physical accuracy.

Multiscale Diffusion Monte Carlo Simulation of Epitaxial Growth. C.C.Chou, M.L.Falk: Journal of Computational Physics, 2006, 217[2], 519-29