ABSTRACT
The classic equations describing the macroscopic electromagnetic field are called
the Maxwell’s equations. The finite element methods for the Maxwell’s equations
and the associated eigenvalue problem have been studied by many researchers [42,
164, 226, 43, 38, 113, 72, 147, 39, 202, 35]. For example, discontinuous Galerkin
methods are considered in [58, 2, 59], non-conforming Maxwell’s eigensolvers are
discussed in [51], mixed methods are discussed in detail by Boffi in [38, 35], and
nodal elements are used by electric engineers [77, 110]. Note that for non-convex
polyhedra, nodal elements might lead to spurious eigenvalues [42, 176, 177] and a
suitable remedy is needed [29, 99, 100, 101].
