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We discuss results that have been obtained from the implementation of the initial round of testbeds for numerical relativity which was proposed in the first paper of the Apples with Apples Alliance.
The dynamics of general relativity
Richard Arnowitt, Stanley Deser, and Charles W. Misner · 1962
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The two body problem in geometrodynamics
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Phys. Rev. Lett
R. H. Gowdy · 1971
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Methods for the approximate solution of time dependent problems
Heinz Otto Kreiss and Joseph Oliger · 1973
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Supersonic flows and shock waves
R. Courant and K. O. Friedrichs · 1976
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Kinematics and dynamics of general relativity
James W. York · 1979
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General relativistic collapse to black holes and gravitational waves from black holes
Takashi Nakamura, Ken-ichi Oohara, and Yasufumi Kojima · 1987
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Methods in 3D numerical relativity
Takashi Nakamura and Ken-ichi Oohara · 1989
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Summation by parts for finite differencing approximations for d/dx
B. Strand · 1994
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Time dependent problems and difference methods
Bertil Gustafsson, Heinz-Otto Kreiss, and Joseph Oliger · 1995
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Evolution of three-dimensional gravitational waves: Harmonic slicing case
Masaru Shibata and Takashi Nakamura · 1995
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Note on the propagation of the constraints in standard 3+1 general relativity
Simonetta Frittelli · 1997
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On the numerical integration of Einstein’s field equations
Thomas W. Baumgarte and Stuart L. Shapiro · 1999
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The initial boundary value problem for Einstein’s vacuum field equations
Helmut Friedrich and Gabriel Nagy · 1999
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Towards a stable numerical evolution of strongly gravitating systems in general relativity: The conformal treatments
Miguel Alcubierre, Bernd Brügmann, Thomas Dramlitsch, José A. Font, Philippos Papadopoulos, Edward Seidel, Nikolaos Stergioulas, and Ryoji Takahashi · 2000
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Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
L. E. Kidder, Mark A. Scheel, and Saul A. Teukolsky · 2001
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Convergence and stability in numerical relativity
G. Calabrese, J. Pullin, O. Sarbach, and M. Tiglio · 2002
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Asymptotic behavior of a class of expanding gowdy spacetimes
B.K. Berger · 2002
Cited alongside, same era.
In L. Fernández and L. Manuel González, editors, Current trends in relativistic astrophysics
Sascha Husa · 2002
Cited alongside, same era.
Harmonic coordinate method for simulating generic singularities
David Garfinkle · 2002
Cited alongside, same era.
Exploiting gauge and constraint freedom in hyperbolic formulations of Einstein’s equations
O. Sarbach and M. Tiglio · 2002
Cited alongside, same era.
On a wave map equation arising in general relativity
H. Ringstrom · 2003
Cited alongside, same era.
Well-posed initial-boundary evolution in general relativity
B. Szilágyi and Jeffrey Winicour · 2003
Cited alongside, same era.
Toward the numerical implementation of well-posed, constraint preserving evolution systems for general relativity
D. Alic · 2005
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Well-posed formulations and stable finite differencing schemes for numerical relativity
Ian Hinder · 2005
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Accurate black hole evolutions by fourth-order numerical relativity
Y. Zlochower, J. G. Baker, M. Campanelli, and C. O. Lousto · 2005
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Multi-block simulations in general relativity: high order discretizations, numerical stability, and applications
Luis Lehner, Oscar Reula, and Manuel Tiglio · 2005
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Accurate evolutions of orbiting black-hole binaries without excision
Manuela Campanelli, Carlos O. Lousto, Pedro Marronetti, and Yosef Zlochower · 2006
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Gauge conditions for long-term numerical black hole evolutions without excision
Miguel Alcubierre, Bernd Brügmann, Peter Diener, Michael Koppitz, Denis Pollney, Edward Seidel, and Ryoji Takahashi · 2003
Cited alongside, same era.
Towards standard testbeds for numerical relativity
Miguel Alcubierre, Gabrielle Allen, Thomas W. Baumgarte, Carles Bona, David Fiske, Tom Goodale, Francisco Siddhartha Guzmán, Ian Hawke, Scott Hawley, Sascha Husa, Michael Koppitz, Christiane Lechner, Lee Lindblom, Denis Pollney, David Rideout, Marcelo Salgado, Erik Schnetter, Edward Seidel, Hisa aki Shinkai, Deirdre Shoemaker, Béla Szilágyi, Ryoji Takahashi, and Jeffrey Winicour · 2004
Cited alongside, same era.
On the well posedness of the Baumgarte-Shapiro- Shibata-Nakamura formulation of Einstein’s field equations
Horst Beyer and Olivier Sarbach · 2004
Cited alongside, same era.
Symmetric hyperbolic form of systems of second-order evolution equations subject to constraints
C. Gundlach and J.M. Martin-Garcia · 2004
Cited alongside, same era.
Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations
Carsten Gundlach and Jose M. Martin-Garcia · 2004
Cited alongside, same era.
Strongly hyperbolic second order Einstein’s evolution equations
G. Nagy, O. E. Ortiz, and O. A. Reula · 2004
Cited alongside, same era.
John G. Baker, Joan Centrella, Dae-Il Choi, Michael Koppitz, and James van Meter · 2006
Later among the works it cites.
Hyperbolicity of second-order in space systems of evolution equations
Carsten Gundlach and Jose M. Martin-Garcia · 2006
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Numerical stability for finite difference approximations of Einstein’s equations
Gioel Calabrese, Ian Hinder, and Sascha Husa · 2006
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Finite difference schemes for second order systems describing black holes
Mohammad Motamed, M. C. Babiuc, B. Szilagyi, H-O. Kreiss, and J.Winicour · 2006
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Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
Carsten Gundlach and Jose M. Martin-Garcia · 2006
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Some mathematical problems in numerical relativity
Maria C. Babiuc, Béla Szilágyi, and J. Winicour · 2006
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Testing numerical relativity with the shifted gauge wave
Maria C. Babiuc, Béla Szilágyi, and Jeffrey Winicour · 2006
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Harmonic initial-boundary evolution in general relativity
Maria C. Babiuc, Béla Szilágyi, and J.Winicour · 2006
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Stable radiation-controlling boundary conditions for the generalized harmonic einstein equations
Oliver Rinne · 2006
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Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations
Sascha Husa, Ian Hinder, and Christiane Lechner · 2006
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Testing the accuracy and stability of spectral methods in numerical relativity
M. Boyle, L. Lindblom, H. Pfeiffer, M. Scheel, and L. Kidder · 2007
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Excision without excision
David Brown, Olivier Sarbach, Erik Schnetter, Manuel Tiglio, Peter Diener, Ian Hawke, and Denis Pollney · 2007
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