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Conventional numerical electromagnetic methods are known to provide accurate means of characterizing wireless channel transfer functions. However, their practical utilization is hampered by their typically large computational cost compared to empirical, measurement-based or ray-tracing techniques. In this paper, a full-wave, time-domain technique, stemming from the spatial expansion of electromagnetic field components in smooth, spline-type basis functions, is shown to provide a rigorous, yet efficient tool for site-specific indoor channel modeling. Based on this method, wireless propagation across indoor channel geometries can be accurately characterized and signal fading statistics can be extracted. Numerical examples, indicating the significantly improved efficiency of the proposed approach, compared to the standard finite-difference time-domain method, are given. Moreover, important wave propagation effects on indoor channel performance, readily accounted for by our full-wave analysis, are demonstrated.