A non-linear hybrid finite element formulation, for the three dimensional eigen-value analysis of open cavities is proposed. The infinite solution domain is truncated using a separation surface-S f. Inside the surface-S f the electromagnetic field is formulated employing the finite element technique. Outside the surface-S f the infinite free space domain is modeled through an "infinite" sum of spherical harmonics. The two field expressions, the numerical inside (subdomain-II) the fictitious surface and the analytical one outside (subdomain-I) are bind together by enforcing the "exact" field continuity conditions strictly following a vector Dirichletto-Neumann map formalism. Thus, the "transparency" of the fictitious surface is ensured. The overall procedure ends up to a nonlinear eigenvalue problem for the unknown resonant wavenumber κ r. For the solution of the nonlinear eigenvalue problem the Regula Falsi method is considered. The solution procedure is based on the initial values provided from the resonances of an equivalent closed cavity. The validity of the method is tested against the results of a commercial simulator and is verified through a comparison with results presented in the bibliography.
