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A DG Space–Time Domain Decomposition Method

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Domain Decomposition Methods in Science and Engineering XX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Summary

In this paper we present a hybrid domain decomposition approach for the parallel solution of linear systems arising from a discontinuous Galerkin (DG) finite element approximation of initial boundary value problems. This approach allows a general decomposition of the space–time cylinder into finite elements, and is therefore applicable for adaptive refinements in space and time.

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Bibliography

  1. B. Cockburn, J. Gopalakrishnan, and R. Lazarov. Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal., 47:1319–1365, 2009.

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  4. M. Neumüller and O. Steinbach. Refinement of flexible space–time finite element meshes and discontinuous Galerkin methods. Comput. Visual. Sci., 14:189–205, 2011.

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  5. B. Rivière. Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations. SIAM, Philadelphia, 2008.

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Acknowledgements

This work was supported by the Austrian Science Fund (FWF) within the SFB Mathematical Optimization and Applications in Biomedical Sciences.

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Authors and Affiliations

  1. Institute of Computational Mathematics, TU Graz, Steyrergasse 30, 8010, Graz, Austria

    Martin Neumüller & Olaf Steinbach

Authors
  1. Martin Neumüller
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  2. Olaf Steinbach
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Corresponding author

Correspondence to Martin Neumüller .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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Neumüller, M., Steinbach, O. (2013). A DG Space–Time Domain Decomposition Method. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_74

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