Stability of the puncture method with a generalized Baumgarte-Shapiro-Shibata-Nakamura formulation
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1.
University of Lisbon
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2.
Friedrich Schiller University Jena
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3.
Institute of Space Sciences
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4.
California Institute of Technology
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5.
University of Mississippi
Abstract
The puncture method for dealing with black holes in the numerical simulation of vacuum spacetimes is remarkably successful when combined with the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein equations. We examine a generalized class of formulations modeled along the lines of the Laguna-Shoemaker system and including BSSN as a special case. The formulation is a two parameter generalization of the choice of variables used in standard BSSN evolutions. Numerical stability of the standard finite difference methods is proven for the formulation in the linear regime around flat space, a special case of which is the numerical stability of BSSN. Numerical evolutions are presented and compared with a standard BSSN implementation. Surprisingly, a significant portion of the parameter space yields (long-term) stable simulations, including the standard BSSN formulation as a special case. Furthermore, nonstandard parameter choices typically result in smoother behavior of the evolution variables close to the puncture.
Additional Information
© 2011 American Physical Society. Received 22 November 2010; published 20 May 2011. The authors are grateful to Emanuele Berti, Bernd Brügmann, Ian Hinder, Ronny Richter and Olivier Sarbach for helpful comments on the manuscript. H.W.'s work was partly supported by DFG Grant No. SFB/ Transregio7 and by Fundação para a Ciência e a Tecnologia (FCT)-Portugal through Grant No. SFRH/BD/46061/2008 and through Project Nos. PTDC/FIS/ 098032/2008, PTDC/FIS/098025/2008 and CERN/FP/116341/2010. D.H. was supported partly by DFG Grant No. SFB/Transregio7. U. S. acknowledges support from the Ramón y Cajal Programme of the Spanish Ministry of Science and Innovation (MICINN) as well as FCT-Portugal through Project No. PTDC/FIS/098025/2008, the Sherman Fairchild Foundation to Caltech, by NSF Grant Nos. PHY-0601459, PHY-0652995, PHY-1057238, by loni_numrel05, allocations through the TeraGrid Advanced Support Program under Grant Nos. PHY-090003 and AST- 100021 on NICS' Kraken and SDSC's Trestles clusters and an allocation by the Centro de Supercomputación de Galicia (CESGA) under Project Nos. ICTS-CESGA 120 and ICTS-CESGA 175 on Finis Terae. This work was also supported by NSF Grant No. PHY-0900735 and by the DyBHo–256667 ERC Starting Grant. Computations were partly performed at the LRZ Munich, Milipeia in Coimbra and Magerit in Madrid. The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the Barcelona Supercomputing Centre-Centro Nacional de Supercomputación.Attached Files
Published - Witek2011p14002Phys_Rev_D.pdf
Files
Witek2011p14002Phys_Rev_D.pdf
Additional details
Identifiers
- Eprint ID
- 23934
- Resolver ID
- CaltechAUTHORS:20110607-113734673
Funding
- Deutsche Forschungsgemeinschaft (DFG)
- SFB/Transregio7
- Fundação para a Ciência e a Tecnologia (FCT)
- SFRH/ BD/46061/2008
- Fundação para a Ciência e a Tecnologia (FCT)
- PTDC/FIS/ 098032/2008
- Fundação para a Ciência e a Tecnologia (FCT)
- PTDC/FIS/098025/2008
- Fundação para a Ciência e a Tecnologia (FCT)
- CERN/FP/116341/2010
- Ramón y Cajal Programme
- Sherman Fairchild Foundation
- NSF
- PHY-0601459
- NSF
- PHY-0652995
- NSF
- PHY-1057238
- NSF
- PHY-090003
- NSF
- AST-100021
- Centro de Supercomputación de Galicia (CESGA)
- ICTS-CESGA 120
- Centro de Supercomputación de Galicia (CESGA)
- ICTS-CESGA 175
- NSF
- PHY-0900735
- European Research Council (ERC)
- DyBHo–256667
Dates
- Created
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2011-06-07Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field