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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


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.

Volltext §
DOI: 10.5445/IR/1000060072
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2016
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000060072
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 29 S.
Serie CRC 1173 ; 2016/24
Schlagwörter numerical homogenization, Maxwell’s equations, heterogeneous multiscale method, edge finite elements, two-scale convergence, T-coercivity
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