The geometric average of curl-free fields in periodic geometries
| dc.contributor.author | Poelstra, Klaas Hendrik | |
| dc.contributor.author | Schweizer, Ben | |
| dc.contributor.author | Urban, Maik | |
| dc.date.accessioned | 2019-08-02T12:56:18Z | |
| dc.date.available | 2019-08-02T12:56:18Z | |
| dc.date.issued | 2019-05-31 | |
| dc.description.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 | en |
| dc.identifier.uri | http://hdl.handle.net/2003/38158 | |
| dc.identifier.uri | https://doi.org/10.17877/DE290R-20137 | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | Preprint;2019-05 | |
| dc.subject | periodic homogenization | en |
| dc.subject | Maxwell’s equations | en |
| dc.subject.ddc | 610 | |
| dc.title | The geometric average of curl-free fields in periodic geometries | en |
| dc.type | Text | de |
| dc.type.publicationtype | preprint | en |
| dcterms.accessRights | open access | |
| eldorado.secondarypublication | false |