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Domain Decomposition for Boundary Integral Equations via Local Multi-Trace Formulations

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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 review the ideas behind and the construction of so-called local multi-trace boundary integral equations for second-order boundary value problems with piecewise constant coefficients. These formulations have received considerable attention recently as a promising domain-decomposition approach to boundary element methods.

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Notes

  1. 1.

    As usual, \(H(\varDelta,\varOmega ):=\{ U \in H^{1}(\varOmega ):\,\varDelta U \in L^{2}(\varOmega )\}\).

  2. 2.

    Fraktur font is used to designate functions in the Cauchy trace space, whereas Roman typeface is reserved for Dirichlet traces, and Greek symbols for Neumann traces.

  3. 3.

    By Cauchy trace spaces we mean combined Dirichlet and Neumann traces.

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Author information

Authors and Affiliations

  1. Seminar for Applied Mathematics, ETH Zurich, CH-8092, Zürich, Switzerland

    Ralf Hiptmair

  2. Escuela de Ingeniería, Pontificia Universidad Católica de Chile, Santiago, Chile

    Carlos Jerez-Hanckes

  3. ElectroScience Laboratory, The Ohio State University, Columbus, OH, USA

    Jin-Fa Lee

  4. University of New Mexico, Albuquerque, NM, USA

    Zhen Peng

Authors
  1. Ralf Hiptmair
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  2. Carlos Jerez-Hanckes
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  3. Jin-Fa Lee
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  4. Zhen Peng
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Corresponding author

Correspondence to Ralf Hiptmair .

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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Hiptmair, R., Jerez-Hanckes, C., Lee, JF., Peng, Z. (2014). Domain Decomposition for Boundary Integral Equations via Local Multi-Trace Formulations. 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_4

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