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On the approximation of electromagnetic fields by edge finite elements. Part 2: A heterogeneous ultiscale method for Maxwell’s equations

Ciarlet, Patrick; Fliss, Sonia; Stohrer, Christian

Abstract: In the second part of this series of papers we consider highly oscillatory media. In this situation, the need for a triangulation that resolves all microscopic details of the medium makes standard edge finite elements impractical because of the resulting tremendous computational load. On the other hand, undersampling by using a coarse mesh might lead to inaccurate results. To overcome these diffculties and to improve the ratio between accuracy and computational costs, homogenization techniques can be used. In this paper we recall analytical homogenization results and propose a novel numerical homogenization scheme for Maxwell's equations in frequency domain. This scheme follows the design principles of heterogeneous multiscale methods. We prove convergence to the effective solution of the multiscale Maxwell's equations in a periodic setting and give numerical experiments in accordance to the stated results.

Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000060072
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-600725
KITopen ID: 1000060072
Verlag KIT, Karlsruhe
Umfang 29 S.
Serie CRC 1173 ; 2016/24
Schlagworte numerical homogenization, Maxwell’s equations, heterogeneous multiscale method, edge finite elements, two-scale convergence, T-coercivity
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