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Fuzzy Domain Decomposition: A New Perspective on Heterogeneous DD Methods

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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

In this paper we introduce a new perspective on heterogeneous DD methods. Using fuzzy sets, we define Fuzzy Domain Decomposition Methods (FDDM). We then apply this new coupling method to a very simple, but relevant, advection dominated diffusion problem. We show that the approximation quality of this coupling methodology compares well to the best known coupling methods for this problem. We also provide some numerical results that match very well the analytical prediction.

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Author information

Authors and Affiliations

  1. Université de Genève, 2-4 rue du Lièvre, CP 64, CH-1211, Genève 4, Switzerland

    Martin J. Gander & Jérôme Michaud

Authors
  1. Martin J. Gander
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  2. Jérôme Michaud
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Corresponding author

Correspondence to Jérôme Michaud .

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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Gander, M.J., Michaud, J. (2014). Fuzzy Domain Decomposition: A New Perspective on Heterogeneous DD Methods. 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_23

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