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Brenner, Susanne C.; Li, Fengyan; Sung, Li-Yeng

Nonconforming Maxwell eigensolvers. (English) Zbl 1203.65236

J. Sci. Comput. 40, No. 1-3, 51-85 (2009).
Summary: 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 \(H _{0}(\mathrm{curl};\Omega )\cap H(\mathrm{div}^{0};\Omega )\). 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 \(H _{0}(\mathrm{curl};\Omega )\cap H(\mathrm{div}^{0};\Omega)\) in \(L _{2}(\Omega )\). The performance and the relative merits of these eigensolvers are demonstrated through numerical experiments.

Cited in 13 Documents

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory

Keywords:

Maxwell eigenvalues; nonconforming finite element method; interior penalty method; spurious eigenvalues
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References:

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