Constraint propagation revisited - Adjusted ADM formulation for numerical relativity

Hisa Aki Shinkai, Gen Yoneda

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    Formulation of the Einstein equations is one of the necessary implements for realizing long-term stable and accurate numerical simulations. We re-examine our formulation scheme, that intends to construct a dynamical system which evolves toward the constraint surface as the attractor, by adjusting evolution equations with constraints. We propose an additional guideline which may delay the final blow-up. The new idea is to avoid multipliers to the evolution equations which produce non-linear growth of the constraints in the later stage. Slight but actual improvement can be seen in our test simulations.

    Original languageEnglish
    Title of host publicationProceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006
    Pages259-262
    Number of pages4
    Publication statusPublished - 2006
    Event16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006 - Niigata
    Duration: 2006 Nov 272006 Dec 1

    Other

    Other16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006
    CityNiigata
    Period06/11/2706/12/1

    Fingerprint

    relativity
    formulations
    propagation
    multipliers
    Einstein equations
    dynamical systems
    simulation
    adjusting

    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics

    Cite this

    Shinkai, H. A., & Yoneda, G. (2006). Constraint propagation revisited - Adjusted ADM formulation for numerical relativity. In Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006 (pp. 259-262)

    Constraint propagation revisited - Adjusted ADM formulation for numerical relativity. / Shinkai, Hisa Aki; Yoneda, Gen.

    Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006. 2006. p. 259-262.

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Shinkai, HA & Yoneda, G 2006, Constraint propagation revisited - Adjusted ADM formulation for numerical relativity. in Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006. pp. 259-262, 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006, Niigata, 06/11/27.
    Shinkai HA, Yoneda G. Constraint propagation revisited - Adjusted ADM formulation for numerical relativity. In Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006. 2006. p. 259-262
    Shinkai, Hisa Aki ; Yoneda, Gen. / Constraint propagation revisited - Adjusted ADM formulation for numerical relativity. Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006. 2006. pp. 259-262
    @inbook{5abd7c8dcaf141fda29499e8645b3d7c,
    title = "Constraint propagation revisited - Adjusted ADM formulation for numerical relativity",
    abstract = "Formulation of the Einstein equations is one of the necessary implements for realizing long-term stable and accurate numerical simulations. We re-examine our formulation scheme, that intends to construct a dynamical system which evolves toward the constraint surface as the attractor, by adjusting evolution equations with constraints. We propose an additional guideline which may delay the final blow-up. The new idea is to avoid multipliers to the evolution equations which produce non-linear growth of the constraints in the later stage. Slight but actual improvement can be seen in our test simulations.",
    author = "Shinkai, {Hisa Aki} and Gen Yoneda",
    year = "2006",
    language = "English",
    pages = "259--262",
    booktitle = "Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006",

    }

    TY - CHAP

    T1 - Constraint propagation revisited - Adjusted ADM formulation for numerical relativity

    AU - Shinkai, Hisa Aki

    AU - Yoneda, Gen

    PY - 2006

    Y1 - 2006

    N2 - Formulation of the Einstein equations is one of the necessary implements for realizing long-term stable and accurate numerical simulations. We re-examine our formulation scheme, that intends to construct a dynamical system which evolves toward the constraint surface as the attractor, by adjusting evolution equations with constraints. We propose an additional guideline which may delay the final blow-up. The new idea is to avoid multipliers to the evolution equations which produce non-linear growth of the constraints in the later stage. Slight but actual improvement can be seen in our test simulations.

    AB - Formulation of the Einstein equations is one of the necessary implements for realizing long-term stable and accurate numerical simulations. We re-examine our formulation scheme, that intends to construct a dynamical system which evolves toward the constraint surface as the attractor, by adjusting evolution equations with constraints. We propose an additional guideline which may delay the final blow-up. The new idea is to avoid multipliers to the evolution equations which produce non-linear growth of the constraints in the later stage. Slight but actual improvement can be seen in our test simulations.

    UR - http://www.scopus.com/inward/record.url?scp=84887378310&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84887378310&partnerID=8YFLogxK

    M3 - Chapter

    AN - SCOPUS:84887378310

    SP - 259

    EP - 262

    BT - Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006

    ER -