Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisation of the Maxwell eqations

D. Sarmany, Mikhail A. Bochev, Jacobus J.W. van der Vegt

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    Abstract

    Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared to fixed-order schemes. This comes without a significant increase in the computation work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the complete scheme. The analysis also provides practical information on the convergence of the dissipation and dispersion error, which is important when studying wave propagation phenomena.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages31
    Publication statusPublished - 21 Jan 2007

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.2/1821
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • MSC-65L06
    • MSC-65M60
    • EWI-9168
    • METIS-242036
    • MSC-78M10
    • IR-66899

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