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Nonconforming Maxwell Eigensolvers

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Abstract

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(curl;Ω)∩H(div0;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 H 0(curl;Ω)∩H(div0;Ω) in L 2(Ω). The performance and the relative merits of these eigensolvers are demonstrated through numerical experiments.

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Authors and Affiliations

  1. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA

    Susanne C. Brenner

  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Fengyan Li

  3. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Li-yeng Sung

Authors
  1. Susanne C. Brenner
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  2. Fengyan Li
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  3. Li-yeng Sung
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Corresponding author

Correspondence to Fengyan Li.

Additional information

The work of S.C. Brenner was supported in part by the National Science Foundation under Grant No. DMS-07-38028, and Grant No. DMS-07-13835.

The work of F. Li was supported in part by the National Science Foundation under Grant No. DMS-06-52481, and by the Alfred P. Sloan Foundation as an Alfred P. Sloan Research Fellow.

The work of L. Sung was supported in part by the National Science Foundation under Grant No. DMS-07-13835.

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Brenner, S.C., Li, F. & Sung, Ly. Nonconforming Maxwell Eigensolvers. J Sci Comput 40, 51–85 (2009). https://doi.org/10.1007/s10915-008-9266-9

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  • DOI: https://doi.org/10.1007/s10915-008-9266-9

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