This paper proposes to apply a semi-implicit difference scheme where diffusion terms in the time-dependent partial differential equation are discretized implicitly and non-diffusion ones explicitly thus overcoming the prohibitive step-size in lithographic mask optimization (MO). Further, monitoring pixels on mask pattern contour instead of all pattern pixels are selected locally corresponding to high-frequency layout component and optimized to ease the computation complexity. Superior MO performance is demonstrated by the simulation results in terms of improved convergence with reduced optimization dimensionality.