DC FieldValueLanguage
dc.contributor.authorPoelstra, Klaas Hendrik-
dc.contributor.authorSchweizer, Ben-
dc.contributor.authorUrban, Maik-
dc.date.accessioned2019-08-02T12:56:18Z-
dc.date.available2019-08-02T12:56:18Z-
dc.date.issued2019-05-31-
dc.identifier.urihttp://hdl.handle.net/2003/38158-
dc.description.abstractIn 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 tracesen
dc.language.isoen-
dc.relation.ispartofseriesPreprint;2019-05-
dc.subjectperiodic homogenizationen
dc.subjectMaxwell’s equationsen
dc.subject.ddc610-
dc.titleThe geometric average of curl-free fields in periodic geometriesen
dc.typeTextde
dc.type.publicationtypepreprinten
dcterms.accessRightsopen access-