Performance comparison of finite-element approaches for electromagnetic waveguides

The accuracy of finite-element-method techniques used for waveguide modal analysis has usually been assessed by testing the precision of the propagation constant. As a consequence, no useful criteria have been proposed for checking the spatial distribution of the evaluated unknown field. To overcome this lack, two error figures have been introduced and applied to different finite-element-method formulations. In particular, the following approaches have been compared: the one based on the transverse magnetic field, those based on the so-called edge elements, and a new one presented by the authors. The new approach, obtained by simply operating on the matrices of the original node-based formulation, directly solves for the propagation constant at a given frequency, preserves the matrix sparsity, and directly evaluates all of the unknown magnetic field components. Results demonstrate the applicability of the proposed approach and the usefulness of the introduced figures for a deep waveguide analysis.