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In the design of microstrip monolithic integrated circuits and millimeter-wave printed antennas, accurate numerical modeling becomes important as the operating frequency becomes higher. Besides of metallic patches, dielectric antennas are actively studied as alternative radiating elements. Our solution of the scattering by a circular dielectric patch is based on the Method of Regularization combined with the Galerkin's Method. This method has a controlled accuracy in the resonant range, and a much smaller matrix size in comparison to solutions obtained by direct applications of the Method of Moments.