Finite element eigenvalue enclosures for the Maxwell operator

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

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5 Citations (Scopus)
23 Downloads (Pure)

Abstract

We propose employing the extension of the L ehmann-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
DOIs
Publication statusPublished - 2014

Keywords

  • Eigenvalue enclosures
  • Finite element method
  • Maxwell equation
  • Spectral pollution

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

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