Higher Order Spectral Element Method for Rapid Analysis of Eccentric Coaxial Waveguides Filled With Lossy Anisotropic Media

We present a novel higher order spectral element method (SEM) in the cylindrical coordinates to rapidly analyze electromagnetic fields in eccentric coaxial waveguides filled with lossy uniaxially anisotropic media. Our method achieves accurate results with a minimal number of elements and degrees of freedom (DoFs) in a short amount of time. The formulation uses transformation optics (TO) to map the eccentric circular waveguide into an equivalent concentric problem. In addition, we use higher order 2-D basis functions associated with the zeros of the completed Lobatto polynomial to model the fields in the concentric structure. The convergence analysis demonstrates the absence of Runge's phenomenon as the expansion order increases. We validate the proposed approach against an analytical solution using the Bessel-Fourier harmonics supplemented by Graf's addition theorem (GAT), as well as perturbation-based, finite-element-based, and finite-integration-based numerical solutions. The results indicate the superior accuracy and computational efficiency of our solution.