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Direct time domain computation of Maxwell's differential equations will soon become a practical technique because of the availability of supercomputers. The principal methods used in time domain computations and the supporting theories are presented. The point-matched finite element method is chosen as the main feature of this presentation, which includes the discretization of equations, conforming mesh generation, dielectric and metallic interfaces, numerical stability and simulation of radiation conditions. Numerical results of scattering of Gaussian pulses are presented in time sequences.