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An Additive Schwarz Analysis for Multiplicative Schwarz Methods: General Case

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Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

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Abstract

We analyze multiplicative Schwarz methods through the additive Schwarz theory. As a by-product we recover the Xu-Zikatanov identity for the norm of product operators. This extends earlier work by the author on multiplicative Schwarz methods that use symmetric positive definite solvers for the subspace corrections.

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Acknowledgements

This work is supported in part by the National Science Foundation under Grant No. DMS-16-20273. The author would also like to acknowledge the support provided by the Hausdorff Research Institute of Mathematics at Univeristät Bonn during her visit in Spring 2017.

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Authors and Affiliations

  1. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

Authors
  1. Susanne C. Brenner
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Correspondence to Susanne C. Brenner .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

  7. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Olof B. Widlund

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Brenner, S.C. (2018). An Additive Schwarz Analysis for Multiplicative Schwarz Methods: General Case. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_2

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