Authors: | Poelstra, Klaas Hendrik Schweizer, Ben Urban, Maik |
Title: | The geometric average of curl-free fields in periodic geometries |
Language (ISO): | en |
Abstract: | In periodic homogenization problems, one considers a sequence \((u^\eta)_\eta \) of solutions to periodic problems and derives a homogenized equation for an effective quantity $\hat u$. In many applications, $\hat u$ is the weak limit of $(u^\eta)_\eta$, but in some applications $\hat u$ must be defined differently. In the homogenization of Maxwell's equations in periodic media, the effective magnetic field is given by the geometric average of the two-scale limit. The notion of a geometric average has been introduced by Bouchitté and Bourel in [3]; it associates to a curl-free field $Y\setminus \overline{\Sigma} \to \R^3$, where $Y$ is the periodicity cell and $\Sigma$ an inclusion, a vector in $\R^3$. In this article, we extend previous definitions to more general inclusions. The physical relevance of the geometric average is supported by various results, e.g., a convergence property of tangential traces |
Subject Headings: | periodic homogenization Maxwell’s equations |
URI: | http://hdl.handle.net/2003/38158 https://doi.org/10.17877/DE290R-20137 |
Issue Date: | 2019-05-31 |
Appears in Collections: | Preprints der Fakultät für Mathematik Schweizer, Ben Prof. Dr. |
Files in This Item:
File | Description | Size | Format | |
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Preprint 2019-05.pdf | DNB | 576.29 kB | Adobe PDF | View/Open |
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