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A discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD) method based on both discrete system theory and the FDTD method has been developed, which expresses the field response as a convolution of current sources and the impulse response of the FDTD equation system. The DGF-FDTD method presents the FDTD equations in a different perspective from the conventional Yee algorithm. It avoids the computational difficulties such as the need for computation of free-space nodes and absorbing boundary conditions of the classic FDTD method. The ability of the DGF-FDTD method to model on antenna is demonstrated by the modeling of a Yagi-Uda array antenna with considerable saving in memory usage.