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On the Construction of Approximate Boundary Conditions for Solving the Interior Problem of the Acoustic Scattering Transmission Problem

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Book cover Domain Decomposition Methods in Science and Engineering

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 40))

Summary

The construction of accurate generalized impedance boundary conditions for the three-dimensional acoustic scattering problem by a homogeneous dissipative medium is analyzed. The technique relies on an explicit computation of the symbolic asymptotic expansion of the exact impedance operator in the interior domain. An efficient pseudolocalization of this operator based on Padé approximants is then proposed. The condition can be easily integrated in an iterative finite element solver without modifying its performances since the pseudolocal implementation preserves the sparse structure of the linear system. Numerical results are given to illustrate the method.

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References

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Author information

Authors and Affiliations

  1. Mathématiques pour l'Industrie et la Physique, MIP, UMR CNRS 5640, UFR MIG, Université P. Sabatier, 118, route de Narbonne, 31062, Toulouse cedex 4, France

    X. Antoine

  2. Laboratoire de Mathématiques Appliquées pour l'Industrie, Université de Pau et des Pays de l'Adour, Avenue de l'Université, 64000, Pau, France

    H. Barucq

Authors
  1. X. Antoine
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  2. H. Barucq
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Editor information

Editors and Affiliations

  1. Moffett Field, CA

    Timothy J. Barth

  2. Bonn

    Michael Griebel

  3. New York

    David E. Keyes  & Tamar Schlick  & 

  4. Espoo

    Risto M. Nieminen

  5. Leuven

    Dirk Roose

  6. Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, 14195, Berlin, Germany

    Ralf Kornhuber

  7. Department of Mathematics, University of Houston, Philip G. Hoffman Hall 651, 77204-3008, Houston, TX, USA

    Ronald Hoppe

  8. Dassault Aviation, 78 Quai Marcel Dassault Cedex 300, 92552, St. Cloud, France

    Jacques Périaux

  9. Laboratoire Jacques-Louis Lions, Université Paris VI, 175 Rue de Chevaleret, 75013, Paris, France

    Olivier Pironneau

  10. Courant Institute of Mathematical Science, New York University, Mercer Street 251, 10012, New York, USA

    Olof Widlund

  11. Department of Mathematics Eberly College of Science, Pennsylvania Sate University, McAllister Building 218, 16802, University Park, PA, USA

    Jinchao Xu

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© 2005 Springer-Verlag Berlin Heidelberg

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Antoine, X., Barucq, H. (2005). On the Construction of Approximate Boundary Conditions for Solving the Interior Problem of the Acoustic Scattering Transmission Problem. In: Barth, T.J., et al. Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26825-1_9

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