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A hybrid finite-element method/moment method (FEM/MM) is used to analyse a waveguide-fed dielectric resonator antenna with a dielectric constant εra. Green's function for the dielectric hemisphere, rather than the free-space Green's function used in conventional hybrid FEM/MM, is employed to establish the integral equation. To simplify the analysis, two different kinds of basis function are used to discretise the slot field in the FEM and MM, respectively. The accuracy of the hybrid FEM/MM is confirmed by measured data for the special case of one waveguide-fed slot radiator, i.e., εra=1. The numerical results demonstrate that the energy coupling can be greatly improved by placing a dielectric resonator inside the waveguide.