Finite Element Eigenvalue Enclosures for the Maxwell Operator

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 bo...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2014-01, Vol.36 (6), p.A2887-A2906
Main Authors: Barrenechea, G. R., Boulton, L., Boussaïd, N.
Format: Article
Language:English
Subjects:
Asymptotic properties
Computation
Eigenfrequencies
Enclosures
Finite element method
Holes
Mathematical analysis
Mathematical models
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Summary: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 $t\in \mathbb{R}$. 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.
ISSN:1064-8275
1095-7197
DOI:10.1137/140957810