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Optimized Schwarz Methods for Heterogeneous Helmholtz and Maxwell’s Equations

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Domain Decomposition Methods in Science and Engineering XXIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

Abstract

Both the Helmholtz equation and the time-harmonic Maxwell’s equations are difficult to solve by iterative methods in the intermediate to high frequency regime, and domain decomposition methods are among the most promising techniques for this task. We focus here on the case of dissipative and conductive media with strongly heterogeneous coefficients, and develop optimized transmission conditions for this case. We establish a link for the use of such conditions between the case of Helmholtz and Maxwell’s equations, and show that in both cases jumps aligned with the interfaces of the subdomains can improve the convergence of the subdomain iteration.

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Acknowledgements

Hui Zhang was supported by Research Start Funding of Zhejiang Ocean University

Author information

Authors and Affiliations

  1. University of Strathclyde, Glasgow, UK

    Victorita Dolean

  2. University Cote d’Azur, CNRS, LJAD, Nice Cedex 02, France

    Victorita Dolean

  3. Section de mathématiques, Université de Genève, 1211 Genève 4, Geneva, Switzerland

    Martin J. Gander & Erwin Veneros

  4. Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, 316022, Zhoushan, China

    Hui Zhang

Authors
  1. Victorita Dolean
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  2. Martin J. Gander
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  3. Erwin Veneros
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  4. Hui Zhang
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Corresponding author

Correspondence to Victorita Dolean .

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

  4. Dept. of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

  7. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA

    Olof B. Widlund

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Dolean, V., Gander, M.J., Veneros, E., Zhang, H. (2017). Optimized Schwarz Methods for Heterogeneous Helmholtz and Maxwell’s Equations. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_13

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