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In this paper, the finite-volume time-domain (FVTD) method is refined and applied to analyze a probe-fed hemispherical dielectric resonator antenna (DRA). To improve the applicability of the FVTD method to microwave problems, a new scheme is introduced taking advantage of the method's inherent flux separation into incoming and outgoing waves. A 3D simulation is performed using an unstructured tetrahedral mesh permitting precise modeling of curved surfaces and fine structures. The obtained results are compared to those from other methods.