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Additive Nonoverlapping Schwarz for h-p Composite Discontinuous Galerkin

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9574))

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Abstract

A second order elliptic problem with piecewise constant coefficient in 2-D or 3-D is considered. The problem is discretized by a composite \(h\)-\(p\) finite element method, using continuous functions in subregions where the coefficient is constant and applying discontinuous Galerkin interior penalty method to couple them. The resulting discrete problem is solved by a two-level nonoverlapping additive Schwarz method. Condition number estimate of the preconditioned system, depending on the relative sizes of the underlying grids and on the relative degrees of finite elements used on the fine and coarse grids, is provided. In particular, the rate of convergence of the method is independent of the jumps of the coefficient.

This research has been partially supported by the Polish National Science Centre grant 2011/01/B/ST1/01179.

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Acknowledgement

The author would like to thank Max Dryja for comments on an early draft of the paper. This research has been partially supported by the Polish National Science Centre grant 2011/01/B/ST1/01179.

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Authors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Piotr Krzyżanowski

Authors
  1. Piotr Krzyżanowski
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Correspondence to Piotr Krzyżanowski .

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Editors and Affiliations

  1. Czestochowa University of Technolog, Czestochowa, Poland

    Roman Wyrzykowski

  2. Department of Computer Science, University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  3. Electrical Engineering & Comput. Science, University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Institute of Computer & Information Sci., Czestochowa, Poland

    Konrad Karczewski

  5. Department of Computer Science, AGH University of Science and Technology, Krakow, Poland

    Jacek Kitowski

  6. Systèmes d’informations, Big Data et Rec, AGH University of Science and Technology, Krakow, Poland

    Kazimierz Wiatr

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Krzyżanowski, P. (2016). Additive Nonoverlapping Schwarz for h-p Composite Discontinuous Galerkin. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. Lecture Notes in Computer Science(), vol 9574. Springer, Cham. https://doi.org/10.1007/978-3-319-32152-3_38

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  • DOI: https://doi.org/10.1007/978-3-319-32152-3_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32151-6

  • Online ISBN: 978-3-319-32152-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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