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Stability of the puncture method with a generalized Baumgarte-Shapiro-Shibata-Nakamura formulation

Witek, Helvi and Hilditch, David and Sperhake, Ulrich (2011) Stability of the puncture method with a generalized Baumgarte-Shapiro-Shibata-Nakamura formulation. Physical Review D, 83 (10). Art. No. 104041. ISSN 2470-0010.

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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.

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Sperhake, Ulrich0000-0002-3134-7088
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.
Funding AgencyGrant Number
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 ProgrammeUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Centro de Supercomputación de Galicia (CESGA)ICTS-CESGA 120
Centro de Supercomputación de Galicia (CESGA)ICTS-CESGA 175
European Research Council (ERC)DyBHo–256667
Issue or Number:10
Classification Code:PACS: 04.25.D-, 04.20.Cv, 04.25.dg
Record Number:CaltechAUTHORS:20110607-113734673
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23934
Deposited By: Jason Perez
Deposited On:07 Jun 2011 20:01
Last Modified:03 Oct 2019 02:51

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