Hyperbolic formulations and numerical relativity

II. Asymptotically constrained systems of Einstein equations

Gen Yoneda, Hisa Aki Shinkai

    Research output: Contribution to journalArticle

    29 Citations (Scopus)

    Abstract

    We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously proposed 'λ system', which introduces artificial flows to constraint surfaces based on the symmetric hyperbolic formulation. We show that this system works as expected for the wave propagation problem in the Maxwell system and in general relativity using Ashtekar's connection formulation. Second, we propose a new mechanism to control the stability, which we call the 'adjusted system'. This is simply obtained by adding constraint terms in the dynamical equations and adjusting their multipliers. We explain why a particular choice of multiplier reduces the numerical errors from non-positive or pure-imaginary eigenvalues of the adjusted constraint propagation equations. This 'adjusted system' is also tested in the Maxwell system and in the Ashtekar system. This mechanism affects more than the system's symmetric hyperbolicity.

    Original languageEnglish
    Pages (from-to)441-462
    Number of pages22
    JournalClassical and Quantum Gravity
    Volume18
    Issue number3
    DOIs
    Publication statusPublished - 2001 Feb 7

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    Einstein equations
    relativity
    multipliers
    formulations
    numerical integration
    wave propagation
    eigenvalues
    adjusting
    propagation

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Hyperbolic formulations and numerical relativity : II. Asymptotically constrained systems of Einstein equations. / Yoneda, Gen; Shinkai, Hisa Aki.

    In: Classical and Quantum Gravity, Vol. 18, No. 3, 07.02.2001, p. 441-462.

    Research output: Contribution to journalArticle

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