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In the use of the time-domain integral equation (TDIE) method for the analysis of layered media, it is important to have the time-domain layered medium Green's function computed for many source-to-field distances ρ and time instants t. In this paper, a numerical method is used that computes the mixed potential Green's functions Gv(ρ,t) and GA(ρ,t) for a multilayered medium for many ρ's and t's simultaneously. The method is applicable to multilayered media and for lossless or lossy dispersive media. Salient features of the method are: 1) the use of complex ω so that the surface wave poles are lifted off the real kρ axis such that pole extractions are not required; 2) the use of half-space extraction so that the integrand for the Sommerfeld integral decays exponentially along the kρ axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Green's function is calculated for many values of ρ simultaneously. For a four-layer medium, we illustrate the numerical results by a three-dimensional plot of ρGv(ρ,t) versus ρ and t and demonstrate the space-time evolution of these Green's functions. For a maximum frequency range of 8 GHz, the method requires only a few CPU minutes to compute a table of 100 (points in ρ) × 168 (points in t) uniformly spaced values of Gv(ρ,t) on an 867-MHz Pentium PC.