  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.
