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Maxwell’s equations; eigenvalues; metamaterials; plasmonics; sign-changing coefficients; compatible discretization.
Abstract:
We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing rules were reported, which guarantee the convergence of finite element approximations to the related scalar source problems. Here we generalize these results to the electromagnetic two-dimensional vectorial equations and the related holomorphic eigenvalue problems. Different than for the analysis on the continuous level, we require an assumption on both contrasts of the permittivity and the permeability similar to the three-dimensional case. We confirm our theoretical results with computational studies.
