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arXiv · 1402.4911

Finite element eigenvalue enclosures for the Maxwell operator

Gabriel Raúl Barrenechea·Lyonell Boulton·Nabile 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 real parameter. 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.

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Gabriel Raúl Barrenechea, Lyonell Boulton, Nabile Boussaid. 2014-02-20. Finite element eigenvalue enclosures for the Maxwell operator. https://arxiv.org/abs/1402.4911

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