The mixed spectral element method: a novel approach to remove zero spurious modes in electromagnetics

In this paper, we propose a novel mixed spectral element method (mixed SEM) to remove such zero spurious modes and significantly improve the numerical solutions of the Maxwell eigenvalue problem. We will demonstrate this mixed SEM with the applications in waveguides and cavities. In order to suppress the zero spurious modes, the divergence-free condition (i.e., Gauss' law) must be enforced in the spectral element. The novel high-order mixed SEM is proposed for the analysis of anisotropic, lossy, and open waveguides and cavities. It utilizes the edge-based curl-conforming Gauss-Lobatto-Legendre (GLL) polynomials to approximate the tangential vector of the electric field; and for waveguide problems, it uses the nodal-based scalar GLL basis functions to discretize its longitudinal component to obtain the highly accurate simulations.