Abstract: The FEM exhibits a slow rate of convergence when it is used for analysis of waveguides containing sharp edges where electromagnetic field is singular. The convergence of the method can be improved by introducing singular elements that model analytically predicted singular behavior. A number of authors have developed singular elements that are compatible with either scalar or standard vector FEM. In this paper we propose a new singular element that is compatible with the edge-based finite elements of arbitrary order and can cope with any order of singularity while preserving the sparsity of the FEM equations. All necessary integrations are performed in closed form. Edge-based singular elements not only more correctly model singular behavior of the field and thus require smaller FEM mesh, but they also do not introduce any spurious modes in the numerical solution. Numerical results presented in this paper verify that the convergence of the FEM is significantly improved.
Keywords: Finite element method, waveguide, anisotropic medium, isotropic medium, singular element, L-shaped waveguide.