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Domain Decomposition Methods in Science and Engineering XXI pp 447–455Cite as

Achieving Robustness Through Coarse Space Enrichment in the Two Level Schwarz Framework

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

Abstract

As many DD methods the two level Additive Schwarz method may suffer from a lack of robustness with respect to coefficient variation. This is the case in particular if the partition into is not aligned with all jumps in the coefficients. The theoretical analysis traces this lack of robustness back to the so called stable splitting property. In this work we propose to solve a generalized eigenvalue problem in each subdomain which identifies which vectors are responsible for violating the stable splitting property. These vectors are used to span the coarse space and taken care of by a direct solve while all remaining components behave well. The result is a condition number estimate for the two level method which does not depend on the number of subdomains or any jumps in the coefficients.

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Author information

Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, CNRS UMR 7598, Université Pierre et Marie Curie, 75005, Paris, France

    Nicole Spillane & Frédéric Nataf

  2. Manufacture des Pneumatiques Michelin, 63040, Clermont-Ferrand, Cedex 09, France

    Nicole Spillane & Patrice Hauret

  3. Laboratoire J.-A. Dieudonné, CNRS UMR 6621, Université de Nice-Sophia Antipolis, 06108, Nice Cedex 02, France

    Victorita Dolean

  4. Institute of Computational Mathematics, Johannes Kepler University, Altenberger Str. 69, 4040, Linz, Austria

    Clemens Pechstein

  5. Department of Mathematical Sciences, University of Bath, Bath, BA27AY, UK

    Robert Scheichl

Authors
  1. Nicole Spillane
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  2. Victorita Dolean
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  3. Patrice Hauret
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  4. Frédéric Nataf
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  5. Clemens Pechstein
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  6. Robert Scheichl
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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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Spillane, N., Dolean, V., Hauret, P., Nataf, F., Pechstein, C., Scheichl, R. (2014). Achieving Robustness Through Coarse Space Enrichment in the Two Level Schwarz Framework. 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_42

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