Eigenanalysis of Electromagnetic Structures Based on the Finite Element Method

This article presents a review of our research effort on the eigenanalysis of open radiating waveguides and closed resonating structures. A two dimensional (2-D) hybrid Finite Element method in conjunction with a cylindrical harmonics expansion is established to formulate the open waveguide generalized eigenvalue problem. The key element of this approach refers to the adoption of a vector Dirichlet-to-Neumann map to rigorously enforce the continuity of the two field expansions along a truncation surface. The resulting algorithm was able to evaluate both surface and leaky eigenmodes. The eigenanalysis of three dimensional (3-D) structures involves vast research challenges, especially when they are electrically large and open-radiating. The effort herein is focused on the electrically large case including the losses due to the finite conductivity of metallic walls and objects as well as the loading material losses. The former is introduced through impedance or Leontovich boundary condition, resulting to a non-linear-polynomial generalized eigenvalue problem. A straightforward linearization solution is adopted along with a more efficient alternative technique which mimics analytical approaches. For this one the linear eigenproblem formulated assuming metals as perfect electric conductors is initially solved and their finite conductivity is accounted through impedance boundary conditions enforced locally on the resulting eigenvectors. Finally, some numerical results are presented to verify the performance of these methodologies along with a discussion on their possibilities for extension to open 3D structures as well as to characteristic modes eigenanalysis.