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Domain Decomposition Methods in Science and Engineering XVIII pp 241–248Cite as

The Development of Coarse Spaces for Domain Decomposition Algorithms

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 70))

Summary

The importance of using coarse components, and thus at least one additional level, in the design of domain decomposition methods has been understood for at least twenty years. For many problems of interest, such a device, which provides at least a minimal amount of global transfer of information in each step, is necessary in order to obtain convergence rates which are independent of the number of subdomains. An historical overview, colored by the scientific history of its author, is given of the development of such coarse components of the domain decomposition algorithms. These algorithms are all preconditioned conjugate gradient methods or they are accelerated by using some alternative Krylov space method. The preconditioners are built from solvers of the given problem restricted to subdomains and a coarse approximation which often can be quite exotic.

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Authors and Affiliations

  1. Courant Institute, 251 Mercer Street, New York, NY, 10012, USA

    Olof B. Widlund

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  1. Olof B. Widlund
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Correspondence to Olof B. Widlund .

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Editors and Affiliations

  1. School of Computer Science and Engineering, The Hebrew University of Jerusalem, Ross Building - Givat Ram Campus, 91904, Jerusalem, Israel

    Michel Bercovier

  2. Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, 1211, Genève 24, Switzerland

    Martin J. Gander

  3. Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195, Berlin-Dahlem, Germany

    Ralf Kornhuber

  4. Courant Institute, 251 Mercer Street, New York, NY, 10012, USA

    Olof Widlund

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Widlund, O.B. (2009). The Development of Coarse Spaces for Domain Decomposition Algorithms. In: Bercovier, M., Gander, M.J., Kornhuber, R., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XVIII. Lecture Notes in Computational Science and Engineering, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02677-5_26

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