### 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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Title of host publication | Proceedings of the 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009 |

Pages | 363-366 |

Number of pages | 4 |

Publication status | Published - 2009 |

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

### Other

Other | 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009 |
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City | Tokyo |

Period | 09/11/30 → 09/12/4 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

^{2}-Adjusted equations - Another recipe for robust evolution systems. In

*Proceedings of the 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009*(pp. 363-366)

**Constraint propagation of c ^{2}-Adjusted equations - Another recipe for robust evolution systems.** / Tsuchiya, Takuya; Yoneda, Gen; Shinkai, Hisa Aki.

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

^{2}-Adjusted equations - Another recipe for robust evolution systems. in

*Proceedings of the 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009.*pp. 363-366, 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009, Tokyo, 09/11/30.

^{2}-Adjusted equations - Another recipe for robust evolution systems. In Proceedings of the 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009. 2009. p. 363-366

}

TY - GEN

T1 - Constraint propagation of c2-Adjusted equations - Another recipe for robust evolution systems

AU - Tsuchiya, Takuya

AU - Yoneda, Gen

AU - Shinkai, Hisa Aki

PY - 2009

Y1 - 2009

N2 - 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, C2, 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.

AB - 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, C2, 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.

UR - http://www.scopus.com/inward/record.url?scp=84887495429&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887495429&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84887495429

SP - 363

EP - 366

BT - Proceedings of the 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009

ER -