A fem analysis of open boundary structures using edge elements and a cylindrical harmonics expansion

A finite element formulation for the solution of two-dimensional open field problems is proposed. The structure to be analyzed is enclosed in a circular contour C, and a vector electric field formulation based on hybrid node–edge elements is employed inside C, while the field outside C is expanded into an infinite sum of circular harmonics. The weighting factors of the expansion are evaluated by enforcing the field continuity conditions on the contour C. A generalized eigenvalue problem is finally formulated for the propagation constant along the axial direction (β-formulation), which is solved employing the QZ decomposition algorithm. The validity of the proposed method is established through comparisons with numerical and experimental results available in the published literature.