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The Finite-Difference Time-Domain(FDTD)method is a very popular numerical method for solving the Maxwell's equations of electrodynamics.In this talk,we present some of the recently developed FDTD based methods for problems involving complex media,including the anisotropic media for simulating electromagnetic metamaterial cloaking devices,the magnetoelectric material for spacetime cloak,and nonlinear metamaterials for second harmonic generation(SHG).