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

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Part of the book series: Lecture Notes in Computational Science and Engineering ((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.

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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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Authors and Affiliations

  1. Institute of Applied and Numerical Analysis, Karlsruhe Institute of Technology, Englerstrasse 2, 76131, Karlsruhe, Germany

    Marlis Hochbruck & Christian Stohrer

Authors
  1. Marlis Hochbruck
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  2. Christian Stohrer
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Corresponding author

Correspondence to Christian Stohrer .

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Editors and Affiliations

  1. School of Mechanical Engineering, University of Campinas, Campinas, Brazil

    Marco L. Bittencourt

  2. Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    Ney A. Dumont

  3. EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Jan S. Hesthaven

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Hochbruck, M., Stohrer, C. (2017). Finite Element Heterogeneous Multiscale Method for Time-Dependent Maxwell’s Equations. In: Bittencourt, M., Dumont, N., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Lecture Notes in Computational Science and Engineering, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-65870-4_18

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