Improved scaling of temperature-accelerated dynamics using localization

While temperature-accelerated dynamics (TAD) is a powerful method for carrying out non-equilibrium simulations of systems over extended time scales, the computational cost of serial TAD increases approximately as N(3) where N is the number of atoms. In addition, although a parallel TAD method based on domain decomposition [Y. Shim et al., Phys. Rev. B 76, 205439 (2007)] has been shown to provide significantly improved scaling, the dynamics in such an approach is only approximate while the size of activated events is limited by the spatial decomposition size. Accordingly, it is of interest to develop methods to improve the scaling of serial TAD. As a first step in understanding the factors which determine the scaling behavior, we first present results for the overall scaling of serial TAD and its components, which were obtained from simulations of Ag/Ag(100) growth and Ag/Ag(100) annealing, and compare with theoretical predictions. We then discuss two methods based on localization which may be used to address two of the primary "bottlenecks" to the scaling of serial TAD with system size. By implementing both of these methods, we find that for intermediate system-sizes, the scaling is improved by almost a factor of N(1/2). Some additional possible methods to improve the scaling of TAD are also discussed.