High-order accurate discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations

D. Sarmany, F. Izsak, Jacobus J.W. van der Vegt

    Research output: Book/ReportReportProfessional

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    Abstract

    We introduce a high-order accurate discontinuous Galerkin (DG) method for the indefinite frequency-domain Maxwell equations in three spatial dimensions. The novelty of the method lies in the way the numerical flux is computed. Instead of using the more popular local discontinuous Galerkin (LDG) or interior-penalty discontinuous Galerkin (IP-DG) numerical fluxes, we opt for a formulation which makes use of the local lifting operator. This allows us to choose a penalty parameter that is independent of the mesh size and the polynomial order. Moreover, we use a hierarchic construction of $H$(curl)-conforming basis functions, the first-order version of which correspond to the second family of Nédélec elements. We also provide a priori error bounds for our formulation, and carry out three-dimensional numerical experiments to validate the theoretical results.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherNumerical Analysis and Computational Mechanics (NACM)
    Number of pages34
    Publication statusPublished - Jan 2009

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1889
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • Scientific Computing
    • Discontinuous finite element method
    • METIS-263716
    • EWI-14852
    • IR-65285
    • Electromagnetic waves

    Cite this

    Sarmany, D., Izsak, F., & van der Vegt, J. J. W. (2009). High-order accurate discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations. Enschede: Numerical Analysis and Computational Mechanics (NACM).
    Sarmany, D. ; Izsak, F. ; van der Vegt, Jacobus J.W. / High-order accurate discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations. Enschede : Numerical Analysis and Computational Mechanics (NACM), 2009. 34 p.
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    abstract = "We introduce a high-order accurate discontinuous Galerkin (DG) method for the indefinite frequency-domain Maxwell equations in three spatial dimensions. The novelty of the method lies in the way the numerical flux is computed. Instead of using the more popular local discontinuous Galerkin (LDG) or interior-penalty discontinuous Galerkin (IP-DG) numerical fluxes, we opt for a formulation which makes use of the local lifting operator. This allows us to choose a penalty parameter that is independent of the mesh size and the polynomial order. Moreover, we use a hierarchic construction of $H$(curl)-conforming basis functions, the first-order version of which correspond to the second family of N{\'e}d{\'e}lec elements. We also provide a priori error bounds for our formulation, and carry out three-dimensional numerical experiments to validate the theoretical results.",
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    Sarmany, D, Izsak, F & van der Vegt, JJW 2009, High-order accurate discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations. Numerical Analysis and Computational Mechanics (NACM), Enschede.

    High-order accurate discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations. / Sarmany, D.; Izsak, F.; van der Vegt, Jacobus J.W.

    Enschede : Numerical Analysis and Computational Mechanics (NACM), 2009. 34 p.

    Research output: Book/ReportReportProfessional

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    AB - We introduce a high-order accurate discontinuous Galerkin (DG) method for the indefinite frequency-domain Maxwell equations in three spatial dimensions. The novelty of the method lies in the way the numerical flux is computed. Instead of using the more popular local discontinuous Galerkin (LDG) or interior-penalty discontinuous Galerkin (IP-DG) numerical fluxes, we opt for a formulation which makes use of the local lifting operator. This allows us to choose a penalty parameter that is independent of the mesh size and the polynomial order. Moreover, we use a hierarchic construction of $H$(curl)-conforming basis functions, the first-order version of which correspond to the second family of Nédélec elements. We also provide a priori error bounds for our formulation, and carry out three-dimensional numerical experiments to validate the theoretical results.

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    KW - Discontinuous finite element method

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    KW - IR-65285

    KW - Electromagnetic waves

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    Sarmany D, Izsak F, van der Vegt JJW. High-order accurate discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations. Enschede: Numerical Analysis and Computational Mechanics (NACM), 2009. 34 p.