A hybrid domain decomposition and truncation method of eigenfunction expansion for the analysis of closed cavities

A hybridization of a domain decomposition and domain truncation method based on Dirichlet to Neumann map is presented. The electromagnetic field inside any inhomogeneity/perturbation is formulated employing the finite element technique. For the remaining interior volume inside the cavity, the field is expanded into a superposition of TE and TM mode analytical eigenfunctions of the empty cavity. The two field expressions, inside (subdomain II) the fictitious boxes (numerical FEM) and the analytical one outside (subdomain I) them, are bind together by enforcing the “exact” field continuity conditions strictly following a vector Dirichlet-to-Neumann map formalism. Thus the “transparency” of these fictitious surfaces is ensured. To decouple the degrees of freedom in the numerical and analytical expansions, equivalent electric and magnetic current densities are considered on the fictitious boxes surface, which result from Love´s equivalence principle. This procedure yields a generalized eigenvalue problem with just a few hundred of degrees of freedom formulated for the cavity resonant frequencies. The methodology is validated against the classical FEM eigenanalysis (entire domain discretization) as well as against analytical solutions.