A Novel High-Order Spectral Element Method for the Analysis of Cylindrical Waveguides Filled with Complex Anisotropic Media

We present an improved formulation of the spectral element method in cylindrical coordinates for analyzing electromagnetic fields in waveguides filled with complex (non-reciprocal and non-Hermitian) anisotropic media. Our method obtains accurate results with a small number of elements and degrees of freedom (DoFs) when compared with ordinary finite-element approaches. For this, we use high-order expansion functions in which the internal nodes of each element are defined by the zeros of the completed Lobatto polynomial. The convergence analysis demonstrates the absence of the Runge effect as the expansion order increases. Numerical results show that our technique is efficient and accurate for modeling cylindrical waveguided geometries filled with complex media.