Testing numerical evolution with the shifted gauge wave

Classical and Quantum Gravity

Volumn 23, Issue 16, 2006, Pages

  Babiuc, Maria C ^a   Sziĺgyi, Béla ^b   Winicour, Jeffrey ^a,b  

^a UNIVERSITY OF PITTSBURGH   (United States)

^b ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746607344     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/23/16/S03     Document Type: Article

References (30)

1. Matzner R A, Seidel H E, Shapiro S L, Smarr L, Suen W-M, Teukolsky S A and Winicour J 1995 Geometry of a black hole collision Science 270 941
2. Abrahams A et al 1998 Schwarzschild perturbative gravitational wave extraction and outer boundary conditions Phys. Rev. Lett. 80 1812
3. Gómez R et al 1998 Stable characteristic evolution of generic three-dimensional single-black-hole spacetimes Phys. Rev. Lett. 80 3915
4. Post D E and Kendall R P 2004 Int. J. High Perform. Comput. Appl. 18 399
5. Post D E and Votta L G 2005 Computational science demands a new paradigm Phys. Today 58 35
6. Alcubierre M et al (The AppleswithApples Alliance) 2004 Towards standard testbeds for numerical relativity Class. Quantum Grav. 589
7. www.appleswithapples.org
8. The AppleswithApples Alliance, Implementation of standard testbeds for numerical relativity (in preparation)
9. Friedrich H and Rendall A D 2000 The Cauchy problem for the Einstein equations Einstein's Field Equations and Their Physical Implications: Selected Essays in Honour of Jürgen Ehlers ed B G Schmidt (Berlin: Springer)
10. de Donder T 1921 La Gravifique Einsteinienne (Paris: Gauthiers-Villars)
11. Fock V 1964 The Theory of Space, Time and Gravitation (New York: Macmillan)
12. Foures-Bruhat Y 1952 Theoreme d'existence pour certain systemes d'equations aux deriveés partielles nonlinaires Acta Math. 88 141
13. Babiuc M C, Szilgyi B and Winicour J 2004 Some mathematical problems in numerical relativity Preprint gr-qc/0404092 (Lect. Notes Phys. at press)
14. Szilgyi B and Winicour J 2003 Well-posed initial-boundary evolution in general relativity Phys. Rev. D 68 041501
15. Szilgyi B, Kreiss H-O and Winicour J 2005 Modeling the black hole excision problem Phys. Rev. D 71 104035
16. Bona C, Ledvinka T, Palenzuela C and Zcek M 2003 General-covariant evolution formalism for numerical relativity Phys. Rev. D 67 104005
17. Friedrich H 1996 Hyperbolic reductions for Einstein's equations Class. Quantum Grav. 13 1451
18. Wald R M 1984 General Relativity (Chicago, IL: University of Chicago Press)
19. Fisher A E and Marsden J E 1972 Commun. Math. Phys. 28 1
20. Pretorius F 2005 Numerical relativity using a generalized harmonic decomposition Class. Quantum Grav. 22 425
21. Pretorius F 2005 Evolution of binary black hole spacetimes Phys. Rev. Lett. 95 121101
22. Gundlach C, Martin-Garcia J M, Calabrese G and Hinder I 2005 Constraint damping in the Z4 formulation and harmonic gauge Class. Quantum Grav. 22 3767
23. Alcubierre M and Schutz B 1994 J. Comput. Phys. 112 44
24. Calabrese G 2005 Finite differencing second order systems describing black hole spacetimes Phys. Rev. D 71 027501
25. Calabrese G and Gundlach C 2005 Discrete boundary treatment for the shifted wave equation Preprint gr-qc/0509119
26. Tiglio M, Lehner L and Neilsen D 2004 3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints Phys. Rev. D 70 104018
27. Lehner L, Neilsen D, Reula O and Tiglio M 2004 The discrete energy method in numerical relativity: towards long-term stability Class. Quantum Grav. 21 5819
28. Calabrese G, Lehner L, Reula O, Sarbach O and Tiglio M 2004 Summation by parts and dissipation for domains with excised regions Class. Quantum Grav. 21 5735
29. http://artemis.phyast.pitt.edu
30. Babiuc M C, Szilgyi B and Winicour J 2006 Harmonic initial-boundary evolution in general relativity Phys. Rev. D 73 064017