When the quantum vacuum is polarized by high-intensity fields, it behaves as a complex nonlinear medium. Direct observation of such nonlinear quantum electrodynamics phenomena in high-power laser pulse interactions is a key goal of experiments planned at upcoming laboratories worldwide. Only a full time-dependent, large-scale three-dimensional model can reliably predict detectable signals in this regime. We present a new numerical scheme to replace the standard Yee solvers (FDTD). Developed on the basis of the Lattice Boltzmann Method (LBM), our scheme leverages LBM’s existing parallelization methods, advanced algorithms, and data structures. Through dispersion analysis, we demonstrate the existence of twelve propagation directions with suppressed numerical dispersion.