Finite element Eigenvalue enclosures for the Maxwell operator

G. R. Barrenechea, L. Boulton, N. Boussaid

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Abstract

We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity problem on a bounded region. This method gives complementary bounds for the eigenfrequencies which are adjacent to a given parameter t ∈ R. We present a concrete numerical scheme which provides certified enclosures in a suitable asymptotic regime. We illustrate the applicability of this scheme by means of some numerical experiments on benchmark data using Lagrange elements and unstructured meshes.
Original languageEnglish
Pages (from-to)A2887–A2906
Number of pages20
JournalSIAM Journal on Scientific Computing
Volume36
Issue number6
Early online date10 Dec 2014
DOIs
Publication statusPublished - 2014

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Keywords

  • eigenvalue enclosures
  • finite element method
  • spectral pollution
  • Maxwell equation

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