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We describe an efficient FDTD theme for handling the problem scattering form large objects which may have only partial circular symmetry. The use of the method enables us to analyze geometries whose dimension are large compared to the wavelength, that could not be accommodated in the available computers by using the conventional FDTD. We invoke the reciprocity principle to reduce a class of reflector antenna problems to an equivalent 2 1/2 -D type, even when the composite antenna system satisfies the azimuthal symmetry criterion only partially. Next, we describe how the FDTD is adapted to azimuthally-symmetric geometries, and discuss how we handle some of the problems encountered in the process of modeling the reflector antenna geometry. These problems include: (i) field singularities at the axis; (ii) excitation of a plane wave source; (iii) the use of nonuniform mesh in a cylindrical system; (iv) source excitation problem to minimize spurious reflections from the truncation boundaries; and, (v) extension of the orthogonal 2 1/2 -D algorithm to a conformal FDTD grid so that it can deal with a curved conductor as well dielectric surfaces.