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 language | English |
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Pages (from-to) | A2887-A2906 |
Number of pages | 20 |
Journal | SIAM Journal on Scientific Computing |
Volume | 36 |
Issue number | 6 |
DOIs | |
Publication status | Published - 10 Dec 2014 |
Keywords
- Eigenvalue enclosures
- Finite element method
- Maxwell equation
- Spectral pollution
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
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Lyonell Boulton
- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Mathematics - Professor
Person: Academic (Research & Teaching)