A New Expression for the 3-D Dyadic FDTD-Compatible Green´s Function Based on Multidimensional Z-Transform

In this letter, a new analytic expression for the time-domain discrete Green´s function (DGF) is derived for the 3-D finite-difference time-domain (FDTD) grid. The derivation employs the multidimensional Z-transform and the impulse response of the discretized scalar wave equation (i.e., scalar DGF). The derived DGF expression involves elementary functions only and requires the implementation of a single function in the multiple-precision arithmetic. For its verification, antennas were simulated in the DGF formulation of the FDTD method with the use of the derived expression demonstrating the correctness of the derivation.