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An Algebraic Multigrid Method for an Adaptive Space–Time Finite Element Discretization

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Large-Scale Scientific Computing (LSSC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10665))

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Abstract

This work is devoted to numerical studies on an algebraic multigrid preconditioned GMRES method for solving the linear algebraic equations arising from a space–time finite element discretization of the heat equation using h–adaptivity on tetrahedral meshes. The finite element discretization is based on a Galerkin–Petrov variational formulation using piecewise linear finite elements simultaneously in space and time. In this work, we focus on h–adaptivity relying on a residual based a posteriori error estimation, and study some important components in the algebraic multigrid method for solving the space–time finite element equations.

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Acknowledgements

This work has been supported by the Austrian Science Fund (FWF) under the Grant SFB Mathematical Optimisation and Applications in Biomedical Sciences.

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Authors and Affiliations

  1. Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    Olaf Steinbach & Huidong Yang

Authors
  1. Olaf Steinbach
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  2. Huidong Yang
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Correspondence to Olaf Steinbach .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Steinbach, O., Yang, H. (2018). An Algebraic Multigrid Method for an Adaptive Space–Time Finite Element Discretization. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-73441-5_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73440-8

  • Online ISBN: 978-3-319-73441-5

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