Higher-order mixed spectral element method for Maxwell eigenvalue problem

Conventional edge elements in solving vector Maxwell's equations by the finite element method will lead to the presence of spurious zero eigenvalues. Here we describes a higher order mixed spectral element method (mixed SEM) for the computation of two-dimensional TEz eigenvalue problem of Maxwell's equations. It utilizes Gauss-Lobatto-Legendre (GLL) polynomials as the basis functions in the finite-element framework with the weak divergence condition. It is shown that this method can suppress all spurious zero and nonzero modes and has spectral accuracy with analytic eigenvalues. Numerical results are given on homogeneous and doubly connected cavities to verify its merits.