Two-step Brillouin zone sampling for efficient computation of electron dynamics in solids.

We develop a numerical Brillouin-zone integration scheme for real-time propagation of electronic systems with time-dependent density functional theory. This scheme is based on the decomposition of a large simulation into a set of small independent simulations. The performance of the decomposition scheme is examined in both linear and nonlinear regimes by computing the linear optical properties of bulk silicon and high-order harmonic generation. The decomposition of a large simulation into a set of independent simulations can improve the efficiency of parallel computation by reducing communication and synchronization overhead and enhancing the portability of simulations across a relatively small cluster machine.