The Gautschi time stepping scheme for edge finite element discretization of the Maxwell equations

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

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    Abstract

    For the time integration of edge finite element discretizations of the three-dimensional Maxwell equations, we consider the Gautschi cosine scheme where the action of the matrix function is approximated by a Krylov subspace method. First, for the space-discretized edge finite element Maxwell equations, the dispersion error of this scheme is analyzed in detail and compared to that of two conventional schemes. Second, we show that the scheme can be implemented in such a way that a higher accuracy can be achieved within less computational time (as compared to other implicit schemes). Although the new scheme is unconditionally stable, it is explicit in structure: as an explicit scheme, it requires only the solution of linear systems with the mass matrix.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversiteit Twente, Faculteit Toegepaste Wiskunde
    Publication statusPublished - 2005

    Publication series

    NameMemoranda Mathematical Sciences
    No.1762
    ISSN (Print)1566-7782

    Keywords

    • MSC-15A15
    • MSC-35Q60
    • MSC-37M15
    • METIS-224711
    • MSC-78M10
    • EWI-3582
    • IR-65946
    • MSC-65M12

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