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Finite Element Heterogeneous Multiscale Method for Time-Dependent Maxwell’s Equations

  • Marlis Hochbruck
  • Christian StohrerEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)

Abstract

We propose a Finite Element Heterogeneous Multiscale Method (FE-HMM) for time dependent Maxwell’s equations in second-order formulation in locally periodic materials. This method can approximate the effective behavior of an electromagnetic wave traveling through a highly oscillatory material without the need to resolve the microscopic details of the material. To prove an a-priori error bound for the semi-discrete FE-HMM scheme, we need a new generalization of a Strang-type lemma for second-order hyperbolic equations. Finally, we present a numerical example that is in accordance with the theoretical results.

Keywords

Time dependent Maxwell’s equations Finite element heterogeneous multiscale method Strang-type lemma for hyperbolic PDEs 

Notes

Acknowledgements

We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173 and the Klaus Tschira Stiftung. In addition we thank the anonymous referee for helpful suggestions.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Applied and Numerical AnalysisKarlsruhe Institute of TechnologyKarlsruheGermany

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