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We assess the accuracy of a standard finite-difference time-domain (FDTD) code in the analysis of the near and far-field characteristics of two-dimensional (2-D) models of small-size dielectric lens antennas made of low or high-index materials and fed by the line sources. We consider extended hemielliptic lenses and use the Muller boundary integral equations (MBIE) method as a suitable reference solution. Inaccuracies of FDTD near so-called half-bowtie resonances are detected. Denser meshing reduces the error of FDTD only to a certain level determined by the type of absorbing boundary conditions used and other fine details of the code. Out of these resonances, FDTD code is demonstrated as capable of providing sufficient accuracy in the near and far-field analysis of small-size hemielliptic lenses typical for the millimeter-wave (mm- wave) applications.