Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows

Sander Rhebergen, Jacobus J.W. van der Vegt, H. van der Ven

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    Abstract

    The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of two- and three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization process we therefore choose to minimize the spectral radius of the error transformation operator. We specifically consider optimizing h-multigrid methods with explicit Runge-Kutta type smoothers for second and third order accurate space-time discontinuous Galerkin finite element discretizations of the 2D advection-diffusion equation. The optimized schemes are compared with current h-multigrid techniques employing Runge-Kutta type smoothers. Also, the efficiency of h-, p- and hp-multigrid methods for solving the Euler equations of gas dynamics with a higher order accurate space-time DG method is investigated.
    Original languageUndefined
    Title of host publicationADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications
    EditorsNorbert Kroll, Heribert Bieler, Herman Deconinck, Vincent Couallier, Harmen van der Ven, Kaare Sorensen
    Place of PublicationBerlin
    PublisherSpringer
    Pages257-269
    Number of pages13
    ISBN (Print)978-3-642-03706-1
    DOIs
    Publication statusPublished - Aug 2010

    Publication series

    NameNotes on Numerical Fluid Mechanics and Multidisciplinary Design
    PublisherSpringer-Verlag
    Number113
    Volume113

    Keywords

    • IR-73356
    • METIS-270769
    • EWI-17723
    • Multigrid
    • Discontinuous Galerkin finite element method

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