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Hybrid Domain Decomposition Solvers for the Helmholtz and the Time Harmonic Maxwell’s Equation

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Book cover Domain Decomposition Methods in Science and Engineering XX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Summary

We present hybrid finite element methods for the Helmholtz equation and the time harmonic Maxwell equations, which allow us to reduce the unknowns to degrees of freedom supported only on the element facets and to use efficient iterative solvers for the resulting system of equations. For solving this system, additive and multiplicative Schwarz preconditioners with local smoothers and a domain decomposition preconditioner with an exact subdomain solver are presented. Good convergence properties of these preconditioners are shown by numerical experiments.

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Author information

Authors and Affiliations

  1. Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    M. Huber & J. Schöberl

  2. Institute for Technical Mechanics, Altenbergerstrasse 69, A-4040, Linz, Austria

    A. Pechstein

Authors
  1. M. Huber
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  2. A. Pechstein
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  3. J. Schöberl
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Corresponding author

Correspondence to M. Huber .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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© 2013 Springer-Verlag Berlin Heidelberg

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Huber, M., Pechstein, A., Schöberl, J. (2013). Hybrid Domain Decomposition Solvers for the Helmholtz and the Time Harmonic Maxwell’s Equation. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_32

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