## Abstract

We focus the formulation problem in numerical relativity, propose new sets of evolution equations, and demonstrate some numerical tests. The goal is to construct a robust evolution system against numerical instability during long-term numerical integration in strong gravitational field. One key idea is to adjust the evolution equations with constraint terms, as was systematically formulated by Yoneda and Shinkai. We here apply an adjusting method proposed by Fiske (2004) which uses the norm of constraints, C^{2}, and does not require the background metric for specifying effective Lagrange multipliers. We present sets of evolution equations both in ADM and BSSN formulations and show numerical tests using Gowdy wave propagation. Detail analyses are in progress, but we observe constraint damping effect as expected.

Original language | English |
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Pages | 363-366 |

Number of pages | 4 |

Publication status | Published - 2009 Dec 1 |

Event | 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009 - Tokyo, Japan Duration: 2009 Nov 30 → 2009 Dec 4 |

### Conference

Conference | 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009 |
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Country | Japan |

City | Tokyo |

Period | 09/11/30 → 09/12/4 |

## ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics