KIT | KIT-Bibliothek | Impressum | Datenschutz

Numerical homogenization of time-dependent Maxwell's equations with dispersion effects

Freese, Jan Philip

Abstract (englisch):
This thesis studies the propagation of electromagnetic waves in heterogeneous structures such as metamaterials. The governing equations for this problem are Maxwell's equations with highly oscillatory parameters. We use an analytic homogenization result which yields an effective Maxwell system that involves a convolution integral. This convolution represents dispersive effects that result from the interaction of the wave with the (locally) periodic microscopic structure.

We discretize in space using the Finite Element Heterogeneous Multiscale Method (FE-HMM) and provide a semi-discrete error estimate. The rigorous error analysis in space is supplemented by a rather standard time discretization at the end of which an efficient, fully discrete method is proposed. This method uses a recursive approximation of the convolution that relies on the assumption that the convolution kernel is an exponential function. Eventually, we present numerical experiments both for the microscopic and the macroscopic scale.

Open Access Logo


Volltext §
DOI: 10.5445/IR/1000129214
Veröffentlicht am 04.02.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Hochschulschrift
Publikationsdatum 04.02.2021
Sprache Englisch
Identifikator KITopen-ID: 1000129214
Verlag Karlsruher Institut für Technologie (KIT)
Umfang V, 169 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 25.11.2020
Referent/Betreuer Prof. C. Wieners
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Schlagwörter Maxwell equations, Sobolev equations, dispersion, homogenization, finite element method, heterogeneous multiscale method, time-integration, recursive convolution, error estimates
Relationen in KITopen
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page