HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part II. Optimization of the Runge-Kutta smoother

Jacobus J.W. van der Vegt, Sander Rhebergen

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    Abstract

    Using a detailed multilevel analysis of the complete hp-Multigrid as Smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator. This multilevel analysis is used to optimize the coefficients in the semi-implicit Runge-Kutta smoother, such that the spectral radius of the multigrid error transformation operator is minimal under properly chosen constraints. The Runge-Kutta coefficients for a wide range of cell Reynolds numbers and a detailed analysis of the performance of the hp-MGS algorithm are presented. In addition, the computational complexity of the hp-MGS algorithm is investigated. The hp-MGS algorithm is tested on a fourth order accurate space-time discontinuous Galerkin finite element discretization of the advection-diffusion equation for a number of model problems, which include thin boundary layers and highly stretched meshes, and a non-constant advection velocity. For all test cases excellent multigrid convergence is obtained.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages24
    Publication statusPublished - Oct 2011

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1956
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • Higher order accurate discretizations
    • EWI-20658
    • Multigrid algorithms
    • Multi-level analysis
    • Runge-Kutta methods
    • Discontinuous Galerkin methods
    • METIS-279715
    • Space-time methods
    • MSC-76M10
    • IR-78252
    • MSC-65M60
    • MSC-65M55
    • Fourier analysis

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