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
Issue Date: 2019-05-31
Appears in Collections:Preprints der Fakultät für Mathematik
Schweizer, Ben Prof. Dr.

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