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Domain Decomposition Methods in Science and Engineering XXII pp 471–479Cite as

Schwarz Methods for Second Order Maxwell Equations in 3D with Coefficient Jumps

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Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 104)

Abstract

We study non-overlapping Schwarz Methods for solving second order time-harmonic 3D Maxwell equations in heterogeneous media. Choosing the interfaces between the subdomains to be aligned with the discontinuities in the coefficients, we show for a model problem that while the classical Schwarz method is not convergent, optimized transmission conditions dependent on the discontinuities of the coefficients lead to convergent methods. We prove asymptotically that the resulting methods converge in certain cases independently of the mesh parameter, and convergence can even become better as the coefficient jumps increase.

Keywords

  • Maxwell Equation
  • Transmission Condition
  • Convergence Factor
  • Applied Current Density
  • Mesh Parameter

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. Section de mathématiques, Université de Genève, 1211, Genève 4, Switzerland

    Victorita Dolean, Martin J. Gander & Erwin Veneros

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

Correspondence to Erwin Veneros .

Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Technische Universität München, Garching, Germany

    Thomas Dickopf

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Geométrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. Institute of Computational Science, University of Lugano, Lugano, Switzerland

    Rolf Krause

  5. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Luca F. Pavarino

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Dolean, V., Gander, M.J., Veneros, E. (2016). Schwarz Methods for Second Order Maxwell Equations in 3D with Coefficient Jumps. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_48

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