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A Non-overlapping Quasi-optimal Optimized Schwarz Domain Decomposition Algorithm for the Helmholtz Equation

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Domain Decomposition Methods in Science and Engineering XX

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

Abstract

In this paper, we present a new non-overlapping domain decomposition algorithm for the Helmholtz equation. We are particularly interested in the method introduced by P.-L. Lions [6] for the Laplace equation and extended to the Helmholtz equation by B. Després [3]. However, this latest approach provides slow convergence of the iterative method due to the choice of the transmission conditions. Thus, in order to improve the convergence, several methods were developed [4, 5, 9, 10].

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Bibliography

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Acknowledgements

Y. Boubendir gratefully acknowledges support from NSF through grant No. DMS–1016405. X. Antoine gratefully acknowledges support from the Agence Nationale pour la Recherche (Ref: ANR-09-BLAN-0057-01) and the Fondation de Recherche pour l’Aéronautique et l’Espace (IPPON Project). C. Geuzaine gratefully acknowledges support from the Belgian Science Policy (IAP P6/21), Belgian French Community (ARC 09/14-02) and Walloon Region (WIST3 No 1017086 “ONELAB”).

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, NJIT, Univ. Heights, 323 Dr. M. L. King Jr. Blvd, Newark, NJ, 07102, USA

    Y. Boubendir

  2. Institut Elie Cartan Nancy (IECN), Nancy University, INRIA Corida Team, 239, F-54506, Vandoeuvre-lès-Nancy Cedex, France

    X. Antoine

  3. Department of Electrical Engineering and Computer Science, University of Liège, Montefiore Institute B28, B-4000, Liège, Belgium

    C. Geuzaine

Authors
  1. Y. Boubendir
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  2. X. Antoine
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  3. C. Geuzaine
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Corresponding author

Correspondence to Y. Boubendir .

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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Boubendir, Y., Antoine, X., Geuzaine, C. (2013). A Non-overlapping Quasi-optimal Optimized Schwarz Domain Decomposition Algorithm for the Helmholtz 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_61

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