The Heterogeneous Multiscale Method for dispersive Maxwell systems

In this work, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system contains additional dispersive effects. We provide a carefu...

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Bibliographic Details
Published in:arXiv.org 2021-10
Main Author: Freese, Philip
Format: Article
Language:English
Subjects:
Dispersion
Finite element method
Multiscale analysis
Time dependence
Online Access:Get full text
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Summary:In this work, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system contains additional dispersive effects. We provide a careful study of the (time-dependent) micro problems, including \(\mathrm{H}^2\) and micro errors estimates. Eventually, we prove a semi-discrete error estimate for the method.
ISSN:2331-8422
DOI:10.48550/arxiv.2110.01348