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On the Influence of Curvature on Transmission Conditions

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Book cover Domain Decomposition Methods in Science and Engineering XXI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 98))

Abstract

We are investigating in this short note if and how the curvature of the interfaces influences the choice of transmission conditions in optimized Schwarz methods. We use two approaches: micro-local analysis, and the study of a circular model problem. We find that both approaches lead to transmission conditions which depend on the curvature, and that the transmission conditions based on optimization lead to better convergence than the ones based on micro-local analysis. We illustrate our findings with a simple numerical experiment.

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References

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Acknowledgements

Yingxiang Xu was partly supported by NSFC-11201061 and CPSF-2012M520657.

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Authors and Affiliations

  1. MAGIQUE-3D (INRIA Bordeaux - Sud-Ouest) INRIA-CNRS-Université de Pau et des Pays de l’Adour, BP 1155, F64013, PAU, France

    Hélène Barucq

  2. Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, CP 64, 1211, Genève 4, Switzerland

    Martin J. Gander

  3. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    Yingxiang Xu

Authors
  1. Hélène Barucq
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  2. Martin J. Gander
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  3. Yingxiang Xu
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Corresponding author

Correspondence to Yingxiang Xu .

Editor information

Editors and Affiliations

  1. INRIA, Rennes, France

    Jocelyne Erhel

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

    Martin J. Gander

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

    Laurence Halpern

  4. INRIA, Rennes, France

    Géraldine Pichot

  5. Laboratoire LMNO, Université de Caen, Caen, France

    Taoufik Sassi

  6. New York University Courant Institute, New York, New York, USA

    Olof Widlund

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© 2014 Springer International Publishing Switzerland

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Barucq, H., Gander, M.J., Xu, Y. (2014). On the Influence of Curvature on Transmission Conditions. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_29

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