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The influence of dielectric bodies on electromagnetic fields is a key consideration in many practical engineering problems. In many applications, the scattering from dielectric bodies for known incident fields is of interest. In other situations where a dielectric object interacts with a radiator, such as biological tissue near a wireless transceiver or a dielectric load on an antenna, the resulting input impedance, radiation patterns and power absorption characteristics are important quantities to be determined. Simulation of such configurations often requires the use of computational tools such as the method of moments (MOM) or finite difference time domain (FDTD) approach. Because these techniques are based on different solution methodologies, they provide an independent check of computed results. This paper provides a comparative study of these two approaches. Results from various scattering and radiation examples are presented, and the advantages of each technique are discussed.