Eigenfunction expansion for the analysis of closed cavities

A hybridization of the finite element formulation (FEM) and an eigenfunction expansion for the eigenanalysis of electrically large cavities including small objects - perturbations is proposed. These small objects are enclosed into correspondingly small fictitious boxes and the field inside them is formulated using FEM. For the large cavity field (outside the objects) an expansion into an infinite number of TE and TM modes (eigenfunctions) of the empty cavity is adopted. Equivalent electric and magnetic current densities are considered on each fictitious box surface through Love´s equivalence principle. These are in turn expanded into infinite sums of all possible TE and TM modes, more generally eigenfunctions, of the corresponding box (general field solutions in a 3-D domain). In turn the field continuity conditions on these fictitious surfaces are enforced through the equivalent currents by strictly following the Dirichlet-to-Newmann mathematical formalism. The proposed approach could be considered as a domain-decomposition technique. Finally, the whole procedure yields an eigenvalue problem for the loaded cavity resonant frequencies, which involves only the FEM mesh for the small fictitious boxes. This is in turn solved using the Arnoldi algorithm to yield both resonant frequencies and the modal field distributions. The method is applied for the analysis of numerous loaded cavities and particularly to reverberation chambers.