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This paper presents a novel configuration of a U-shaped, dual-frequency, single-feed, planar inverted-F microstrip antenna with a U-shaped slot (UU-PIFA). The antenna is well suited to telephone handsets used in today's mobile communication systems operating in both GSM and DCS 1800 bands, namely 0.9 and 1.8 GHz, respectively. An initial design is derived from an empirical approximation and a transmission line model of a rectangular microstrip antenna. The paper analyses, examines, and fine-tunes the electrical performance of the antenna, including the return loss, operating frequencies, bandwidths, input impedance, and far-field radiation patterns, by using the generalised non-uniform finite difference time domain (NU-FDTD) Maxwell solver. In addition, to increase the efficiency of the FDTD solver, the concept of domain decomposition is utilised, which enables one to eliminate redundant computational space, and thereby reduce the memory and CPU time requirements.