Constraint propagation in the family of ADM systems

Gen Yoneda, Hisa Aki Shinkai

    Research output: Contribution to journalArticle

    23 Citations (Scopus)

    Abstract

    The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on “asymptotically constrained” systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right-hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of the Fourier component of the constraint propagation equations) are negative or purely imaginary. We show that such a system can be obtained by choosing multipliers of the adjusted terms. Our discussion covers Detweiler’s proposal and Frittelli’s analysis, and we also mention the so-called conformal-traceless ADM systems.

    Original languageEnglish
    Number of pages1
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume63
    Issue number12
    DOIs
    Publication statusPublished - 2001 Jan 1

    Fingerprint

    propagation
    eigenvalues
    multipliers
    Einstein equations
    proposals
    relativity
    formulations
    simulation

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics
    • Physics and Astronomy (miscellaneous)

    Cite this

    Constraint propagation in the family of ADM systems. / Yoneda, Gen; Shinkai, Hisa Aki.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 63, No. 12, 01.01.2001.

    Research output: Contribution to journalArticle

    @article{0befaa45e21544379edb3f7bc1f346a9,
    title = "Constraint propagation in the family of ADM systems",
    abstract = "The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on “asymptotically constrained” systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right-hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of the Fourier component of the constraint propagation equations) are negative or purely imaginary. We show that such a system can be obtained by choosing multipliers of the adjusted terms. Our discussion covers Detweiler’s proposal and Frittelli’s analysis, and we also mention the so-called conformal-traceless ADM systems.",
    author = "Gen Yoneda and Shinkai, {Hisa Aki}",
    year = "2001",
    month = "1",
    day = "1",
    doi = "10.1103/PhysRevD.63.124019",
    language = "English",
    volume = "63",
    journal = "Physical review D: Particles and fields",
    issn = "0556-2821",
    publisher = "American Institute of Physics Publising LLC",
    number = "12",

    }

    TY - JOUR

    T1 - Constraint propagation in the family of ADM systems

    AU - Yoneda, Gen

    AU - Shinkai, Hisa Aki

    PY - 2001/1/1

    Y1 - 2001/1/1

    N2 - The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on “asymptotically constrained” systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right-hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of the Fourier component of the constraint propagation equations) are negative or purely imaginary. We show that such a system can be obtained by choosing multipliers of the adjusted terms. Our discussion covers Detweiler’s proposal and Frittelli’s analysis, and we also mention the so-called conformal-traceless ADM systems.

    AB - The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on “asymptotically constrained” systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right-hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of the Fourier component of the constraint propagation equations) are negative or purely imaginary. We show that such a system can be obtained by choosing multipliers of the adjusted terms. Our discussion covers Detweiler’s proposal and Frittelli’s analysis, and we also mention the so-called conformal-traceless ADM systems.

    UR - http://www.scopus.com/inward/record.url?scp=85038284700&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85038284700&partnerID=8YFLogxK

    U2 - 10.1103/PhysRevD.63.124019

    DO - 10.1103/PhysRevD.63.124019

    M3 - Article

    AN - SCOPUS:0034894136

    VL - 63

    JO - Physical review D: Particles and fields

    JF - Physical review D: Particles and fields

    SN - 0556-2821

    IS - 12

    ER -