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With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems.
Acta Mathematica
Y. Foures-Bruhat · 1952
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The dynamics of general relativity
Richard L. Arnowitt, Stanley Deser, and Charles W. Misner · 1962
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in Sources of gravitational radiation
J. W. York Jr · 1979
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Mathematica: A System for Doing Mathematics by Computer
Stephen Wolfram · 1991
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Time dependent problems and difference methods
Gustaffson, Kreiss, and Oliger · 1995
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Some mathematical and numerical questions connected with first and second order time dependent systems of partial differential equations
Heinz-O. Kreiss and Omar E. Ortiz · 2002
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Illustrating Stability Properties of Numerical Relativity in Electrodynamics
A. M. Knapp, E. J. Walker, and T. W. Baumgarte · 2002
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Harmonic coordinate method for simulating generic singularities
David Garfinkle · 2002
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Elliptic-hyperbolic systems and the einstein equations
L. Andersson and V. Moncrief · 2003
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Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
Carsten Gundlach and José M. Martín-García · 2006
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How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture
James R. van Meter, John G. Baker, Michael Koppitz, and Dae-Il Choi · 2006
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Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. 2nd ed
Ernst Hairer, Christian Lubich, and Gerhard Wanner · 2006
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Mathematical issues in a fully constrained formulation of the einstein equations
Isabel Cordero-Carrión, José María Ibáñez, Eric Gourgoulhon, José Luis Jaramillo, and Jérôme Novak · 2008
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Free and constrained symplectic integrators for numerical general relativity
Ronny Richter and Christian Lubich · 2008
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Strongly Hyperbolic Extensions of the ADM Hamiltonian
J. David Brown · 2008
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BSSN in Spherical Symmetry
J. David Brown · 2008
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Comments on Bona-Masso type slicing conditions in long- term black hole evolutions
David Garfinkle, Carsten Gundlach, and David Hilditch · 2008
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Energy-preserving variant of collocation methods
Ernst Hairer · 2009
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Midpoint rule as a variational-symplectic integrator: Hamiltonian systems
J. David Brown · 2006
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Hyperbolicity of second-order in space systems of evolution equations
Carsten Gundlach and José M. Martín-García · 2006
Cited alongside, same era.
Hyperbolic partial differential equations
Peter Lax · 2006
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Geometry and Regularity of Moving Punctures
Mark Hannam, Sascha Husa, Denis Pollney, Bernd Bruegmann, and Niall O’Murchadha · 2007
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in preparation
Helvi Witek, David Hilditch, and Ulrich Sperhake
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xact: tensor computer algebra
José-María Martín-García
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Strongly hyperbolic Hamiltonian systems in numerical relativity: Formulation and symplectic integration
Ronny Richter · 2009
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Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
Sebastiano Bernuzzi and David Hilditch · 2009
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