Nonconforming Maxwell Eigensolvers

Three Maxwell eigensolvers are discussed in this paper. Two of them use classical nonconforming finite element approximations, and the other is an interior penalty type discontinuous Galerkin method. A main feature of these solvers is that they are based on the formulation of the Maxwell eigenproblem on the space H0(curl; Ω) ∩ H(div; Ω). These solvers are free of spurious eigenmodes and they do not require choosing penalty parameters. Furthermore, they satisfy optimal order error estimates on properly graded meshes, and their analysis is greatly simplified by the underlying compact embedding of H0(curl; Ω)∩H(div ; Ω) in L2(Ω). The performance and the relative merits of these eigensolvers are demonstrated through numerical experiments.