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Two-level Schwarz Methods for Hybridizable Discontinuous Galerkin Methods

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Abstract

In this paper, we propose two-level domain decomposition methods for hybridizable discontinuous Galerkin discretizations including hybridized local discontinuous Galerkin, Raviart–Thomas, and Brezzi–Douglas–Marini finite elements for Poisson’s equation. We study the additive Schwarz method as a preconditioner and the multiplicative method as an iterative solver. In our algorithm, the same discretization scheme is defined on the coarse mesh. In particular, we use the injection operator developed in [13] and prove that the condition number of the preconditioned system only depends on the fraction between coarse and fine mesh sizes and the overlap width. Numerical experiments underline our analytical findings.

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Acknowledgements

This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster). P. Lu has been supported by the Alexander von Humboldt Foundation.

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Authors and Affiliations

  1. Department of Mathematics Sciences, Soochow University, Suzhou, 215006, China

    Peipei Lu

  2. School of Engineering Science, Lappeenranta–Lahti University of Technology, Lappeenranta, Finland

    Andreas Rupp

  3. Interdisciplinary Center for Scientific Computing (IWR) and Mathematics Center Heidelberg (MATCH), Heidelberg University, Mathematikon, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany

    Guido Kanschat

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  1. Peipei Lu
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  2. Andreas Rupp
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Correspondence to Peipei Lu.

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Lu, P., Rupp, A. & Kanschat, G. Two-level Schwarz Methods for Hybridizable Discontinuous Galerkin Methods. J Sci Comput 95, 9 (2023). https://doi.org/10.1007/s10915-023-02121-9

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