On the stability of covariant BSSN formulation

Ryosuke Urakawa; Takuya Tsuchiya; Gen Yoneda

doi:10.1088/1361-6382/ac7e16

On the stability of covariant BSSN formulation

Ryosuke Urakawa, Takuya Tsuchiya^*, Gen Yoneda^*

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

In this study, we investigate the numerical stability of the covariant BSSN (cBSSN) formulation proposed by Brown. We calculate the constraint amplification factor (CAF), which is an eigenvalue of the coefficient matrix of the evolution equations of the constraints on the cBSSN formulation and on some adjusted formulations with constraints added to the evolution equations. The adjusted formulations have a higher numerical stability than the cBSSN formulation from the viewpoint of the CAF.

Original language	English
Article number	165002
Journal	Classical and Quantum Gravity
Volume	39
Issue number	16
DOIs	https://doi.org/10.1088/1361-6382/ac7e16
Publication status	Published - 2022 Aug 18

Keywords

covariant form
eigenvalue analysis
numerical relativity

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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10.1088/1361-6382/ac7e16

Cite this

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abstract = "In this study, we investigate the numerical stability of the covariant BSSN (cBSSN) formulation proposed by Brown. We calculate the constraint amplification factor (CAF), which is an eigenvalue of the coefficient matrix of the evolution equations of the constraints on the cBSSN formulation and on some adjusted formulations with constraints added to the evolution equations. The adjusted formulations have a higher numerical stability than the cBSSN formulation from the viewpoint of the CAF.",

keywords = "covariant form, eigenvalue analysis, numerical relativity",

author = "Ryosuke Urakawa and Takuya Tsuchiya and Gen Yoneda",

note = "Funding Information: We thank referees for carefully reading and giving fruitful comments on our paper. GY and TT were partially supported by JSPS KAKENHI Grant No. 20K03740. GY was partially supported by a Waseda University Grant for Special Research Projects 2021C-138. TT was partially supported by JSPS KAKENHI Grant No. 21K03354, and a Grant for Basic Science Research Projects from The Sumitomo Foundation. Publisher Copyright: {\textcopyright} 2022 The Author(s). Published by IOP Publishing Ltd.",

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AU - Urakawa, Ryosuke

AU - Tsuchiya, Takuya

AU - Yoneda, Gen

N1 - Funding Information: We thank referees for carefully reading and giving fruitful comments on our paper. GY and TT were partially supported by JSPS KAKENHI Grant No. 20K03740. GY was partially supported by a Waseda University Grant for Special Research Projects 2021C-138. TT was partially supported by JSPS KAKENHI Grant No. 21K03354, and a Grant for Basic Science Research Projects from The Sumitomo Foundation. Publisher Copyright: © 2022 The Author(s). Published by IOP Publishing Ltd.

PY - 2022/8/18

Y1 - 2022/8/18

N2 - In this study, we investigate the numerical stability of the covariant BSSN (cBSSN) formulation proposed by Brown. We calculate the constraint amplification factor (CAF), which is an eigenvalue of the coefficient matrix of the evolution equations of the constraints on the cBSSN formulation and on some adjusted formulations with constraints added to the evolution equations. The adjusted formulations have a higher numerical stability than the cBSSN formulation from the viewpoint of the CAF.

AB - In this study, we investigate the numerical stability of the covariant BSSN (cBSSN) formulation proposed by Brown. We calculate the constraint amplification factor (CAF), which is an eigenvalue of the coefficient matrix of the evolution equations of the constraints on the cBSSN formulation and on some adjusted formulations with constraints added to the evolution equations. The adjusted formulations have a higher numerical stability than the cBSSN formulation from the viewpoint of the CAF.

KW - covariant form

KW - eigenvalue analysis

KW - numerical relativity

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On the stability of covariant BSSN formulation

Abstract

Keywords

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