Resonant modes in shielded dielectric resonators are studied by a numerical technique which yields the resonant frequencies, modal field distribution, and Q-factors of various resonant modes, including the hybrid modes. The technique uses field discretization by virtue of dual electric and magnetic grids and allows for a direct numerical solution of the integral form of Maxwell's equation for specified boundary conditions. The details of the matrix formulation are explained on an example of the cavity subdivided into a grid consisting of 3*3 electric cells. A modal field plot exhibiting a spiraling behavior has been observed.
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