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A Two-Level Domain-Decomposition Preconditioner for the Time-Harmonic Maxwell’s Equations

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Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

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Abstract

The construction of fast iterative solvers for the indefinite time-harmonic Maxwell’s system at mid- to high-frequency is a problem of great current interest. Some of the difficulties that arise are similar to those encountered in the case of the mid- to high-frequency Helmholtz equation. Here we investigate how two-level domain-decomposition preconditioners recently proposed for the Helmholtz equation work in the Maxwell case, both from the theoretical and numerical points of view.

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References

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Acknowledgements

This work has been supported in part by the French National Research Agency (ANR), project MEDIMAX, ANR-13-MONU-0012.

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Authors and Affiliations

  1. Université Côte d’Azur, CNRS, LJAD, Nice, France

    Marcella Bonazzoli & Victorita Dolean

  2. University of Strathclyde, Glasgow, UK

    Victorita Dolean

  3. University of Bath, Bath, UK

    Ivan G. Graham

  4. UPMC Univ Paris 06, LJLL, Paris, France

    Euan A. Spence & Pierre-Henri Tournier

Authors
  1. Marcella Bonazzoli
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  2. Victorita Dolean
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  3. Ivan G. Graham
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  4. Euan A. Spence
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  5. Pierre-Henri Tournier
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Corresponding authors

Correspondence to Marcella Bonazzoli , Victorita Dolean , Ivan G. Graham , Euan A. Spence or Pierre-Henri Tournier .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

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

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

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

    Olof B. Widlund

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Bonazzoli, M., Dolean, V., Graham, I.G., Spence, E.A., Tournier, PH. (2018). A Two-Level Domain-Decomposition Preconditioner for the Time-Harmonic Maxwell’s Equations. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_12

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