HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel Analysis

Jacobus J.W. van der Vegt, Sander Rhebergen

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    Abstract

    The hp-Multigrid as Smoother algorithm (hp-MGS) for the solution of higher order accurate space-(time) discontinuous Galerkin discretizations of advection dominated flows is presented. This algorithm combines p-multigrid with h-multigrid at all p-levels, where the h-multigrid acts as smoother in the p-multigrid. The performance of the hp-MGS algorithm is further improved using semi-coarsening in combination with a new semi-implicit Runge-Kutta method as smoother. A detailed multilevel analysis of the hp-MGS algorithm is presented to obtain more insight into the theoretical performance of the algorithm. As model problem a fourth order accurate space-time discontinuous Galerkin discretization of the advection-diffusion equation is considered. The multilevel analysis shows that the hp-MGS algorithm has excellent convergence rates, both for low and high cell Reynolds numbers and on highly stretched meshes.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages35
    Publication statusPublished - Oct 2011

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1955
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • METIS-279714
    • Multigrid algorithms
    • Runge-Kutta methods
    • EWI-20657
    • MSC-65M55
    • MSC-65M60
    • Discontinuous Galerkin methods
    • MSC-76M10
    • Space-time methods
    • Fourier analysis
    • Multi-level analysis
    • IR-78251
    • Higher order accurate discretizations

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  • Cite this

    van der Vegt, J. J. W., & Rhebergen, S. (2011). HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel Analysis. (Memorandum / Department of Applied Mathematics; No. 1955). Enschede: University of Twente, Department of Applied Mathematics.