Mixed Spectral Element Method for 2D Maxwell's Eigenvalue Problem (Communications in Computational Physics, 2020)
It is well known that conventional edge elements in solving vector Maxwell'seigenvalue equations by the finite element method will lead to the presence of spuriouszero eigenvalues. This problem has been addressed for the first order edge elementby Kikuchi by the mixed element method. Inspired by this approach, this paperdescribes a higher order mixed spectral element method (mixed SEM) for the computationof two-dimensional vector eigenvalue problem of Maxwell's equations. Itutilizes Gauss-Lobatto-Legendre (GLL) polynomials as the basis functions in the finite-elementframework with a weak divergence condition. It is shown that this methodcan suppress all spurious zero and nonzero modes and has spectral accuracy. A rigorousanalysis of the convergence of the mixed SEM is presented, based on the higherorder edge element interpolation error estimates, which fully confirms the robustnessof our method. Numerical results are given for homogeneous, inhomogeneous, L-shape,coaxial and dual-inner-conductor cavities to verify the merits of the proposedmethod.