### 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 language | English |
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Title of host publication | Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006 |

Pages | 259-262 |

Number of pages | 4 |

Publication status | Published - 2006 |

Event | 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006 - Niigata Duration: 2006 Nov 27 → 2006 Dec 1 |

### Other

Other | 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006 |
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City | Niigata |

Period | 06/11/27 → 06/12/1 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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.

}

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 -