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%A Evans, C.R.
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%K Numerical relativity

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%K Naked singularities
%K Singularities

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%A Cook, G.B.
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%K Finite difference methods
%K Kerr black holes
%K Partial differential equations
%K Rotating black holes

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%A Alcubierre, M.
%A Brandt, S.
%A Brügmann, B.
%A Gundlach, C.
%A Massó, J.
%A Seidel, E.
%A Walker, P.
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%T Test-beds and applications for apparent horizon finders in numerical relativity
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%K Minimization
%K Multi black hole solutions
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%K Spectral methods
%K Horizons

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%A Alcubierre, M.
%A Brügmann, B.
%A Diener, P.
%A Guzmán, F.S.
%A Hawke, I.
%A Hawley, S.
%A Herrmann, F.
%A Koppitz, M.
%A Pollney, D.
%A Seidel, E.
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%K Black hole collisions
%K Excision
%K Smarr formula
%K Vacuum Einstein equations
%K Innermost stable circular orbits (ISCO)

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%A Andersson, L.
%A Metzger, J.
%9 personal communication
%D 2007
%K Trapped surfaces

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%A Daues, G.
%A Massó, J.
%A Seidel, E.
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%K Scalar fields
%K Boundary conditions

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%A Bernstein, D.
%A Brandt, S.
%A Libson, J.
%A Massó, J.
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%A Walker, P.
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%K Null surfaces

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%A Camarda, K.
%A Libson, J.
%A Massó, J.
%A Seidel, E.
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%T Finding apparent horizons in dynamic 3D numerical spacetimes
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%K Schwarzschild solution

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%A Kleinwächter, A.
%A Meinel, R.
%R 10.1051/0004-6361:20030618
%T Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods
%V 405
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%P 711?721
%J Astron. Astrophys.
%K Relativistic stars
%K Rotation
%K Boundary value problems
%K Nonlinear algebraic equations
%K Relativistic fluids
%K Rotating stars
%K Stationary solutions
%K Neutron stars

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%A Ansorg, M.
%A Brügmann, B.
%A Tichy, W.
%M 064011
%R 10.1103/PhysRevD.70.064011
%T Single-domain spectral method for black hole puncture data
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%J Phys. Rev. D
%K Elliptic equations
%K Linear equations
%K Nonlinear equations
%K Initial value problem

%0 
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%A Ansorg, M.
%M 024018
%R 10.1103/PhysRevD.72.024018
%T Double-domain spectral method for black hole excision data
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%V 72
%D 2005
%J Phys. Rev. D

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%A Petroff, D.
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%R 10.1103/PhysRevD.72.024019
%J Phys. Rev. D
%K Conservation laws

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%A Deser, S.
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%C New York; London
%B Gravitation: An Introduction to Current Research
%T The dynamics of general relativity
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%K Energy and momentum
%K Asymptotically flat data
%K Phase space
%K Cauchy problem
%K Canonical gravity
%K Constraints
%K Constraint equations
%K Gravitation
%K General relativity

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12472
%A Ascher, U.M.
%A Mattheij, R.M.M.
%A Russell, R.D.
%I Prentice-Hall
%D 1988
%C Englewood Cliffs, U.S.A.
%T Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

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%A Ashtekar, A.
%A Beetle, C.
%A Fairhurst, S.
%P L1?L7
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%V 16
%T Isolated horizons: a generalization of black hole mechanics
%R 10.1088/0264-9381/16/2/027
%J Class. Quantum Grav.
%K no keywords
%K Isolated horizons
%K Black hole thermodynamics
%K Dynamical horizons
%K Quasi-local black holes
%K Three-manifolds
%K Trapping horizons
%K Hamiltonian systems

%0 
%U http://relativity.livingreviews.org/refdb/record/4098
%A Ashtekar, A.
%A Krishnan, B.
%M 261101
%D 2002
%V 89
%T Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
%R 10.1103/PhysRevLett.89.261101
%J Phys. Rev. Lett.
%K Area increase law
%K Hamiltonian constraint
%K Killing field
%K Killing horizons

%0 
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%A Ashtekar, A.
%A Krishnan, B.
%M 104030
%D 2003
%V 68
%T Dynamical horizons and their properties
%R 10.1103/PhysRevD.68.104030
%J Phys. Rev. D

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%A Ashtekar, A.
%A Galloway, J.G.
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%V 95
%T Some uniqueness results for dynamical horizons
%J Adv. Theor. Math. Phys.

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%A Ashtekar, A.
%A Krishnan, B.
%D 2004
%M lrr-2004-10
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%T Isolated and Dynamical Horizons and Their Applications
%J Living Rev. Relativity
%K Quantum gravity

%0 
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%A Baiotti, L.
%A Hawke, I.
%A Montero, P.J.
%A Löffler, F.
%A Rezzolla, L.
%A Stergioulas, N.
%A Font, J.A.
%A Seidel, E.
%D 2005
%M 024035
%V 71
%T Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
%R 10.1103/PhysRevD.71.024035
%J Phys. Rev. D
%K Relativity
%K Relativistic hydrodynamics
%K Computational fluid dynamics
%K Finite volume methods
%K Instability
%K Mass formula
%K Relativistic fluid dynamics
%K Numerical relativistic hydrodynamics

%0 Personal Communication
%U http://relativity.livingreviews.org/refdb/record/12475
%A Bartnik, R.
%9 personal communication
%K Inverse mean curvature flow
%K Ricci flow

%0 
%U http://relativity.livingreviews.org/refdb/record/12476
%A Baumgarte, T.W.
%A Cook, G.B.
%A Scheel, M.A.
%A Shapiro, S.L.
%A Teukolsky, S.A.
%R 10.1103/PhysRevD.54.4849
%T Implementing an apparent-horizon finder in three dimensions
%V 54
%D 1996
%P 4849?4857
%J Phys. Rev. D

%0 
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%A Baumgarte, T.W.
%A Shapiro, S.L.
%R 10.1016/S0370-1573(02)00537-9
%T Numerical relativity and compact binaries
%V 376
%D 2003
%P 41?131
%J Phys. Rep.
%K Binary systems

%0 Report
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%A Bernstein, D.
%I National Center for Supercomputing Applications
%C Urbana-Champaign, U.S.A.
%D 1993
%T Notes on the Mean Curvature Flow Method for Finding Apparent Horizons

%0 
%U http://relativity.livingreviews.org/refdb/record/12478
%A Bishop, N.T.
%T The Closed Trapped Region and the Apparent Horizon of Two Schwarzschild Black Holes
%V 14
%D 1982
%P 717?723
%R 10.1007/BF00756083
%J Gen. Relativ. Gravit.

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%A Bishop, N.T.
%T The horizons of two Schwarzschild black holes
%V 16
%D 1984
%P 589?593
%J Gen. Relativ. Gravit.

%0 
%U http://relativity.livingreviews.org/refdb/record/12480
%A Bishop, N.T.
%T The Event Horizons of Two Schwarzschild black holes
%V 20
%D 1988
%P 573?581
%R 10.1007/BF00758912
%J Gen. Relativ. Gravit.
%K Approximation methods

%0 
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%A Bizo?, P.
%A Malec, E.
%A Ó Murchadha, N.
%P 1147?1150
%T Trapped Surfaces in Spherical Stars
%V 61
%D 1988
%J Phys. Rev. Lett.
%K Maximal hypersurfaces
%K Spherical symmetry

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%A Bonazzola, S.
%A Marck, J.-A.
%S Proceedings of the International Workshop on Numerical Relativity, University of Illinois at Urbana-Champaign, USA, May 9 ? 13, 1988
%I Cambridge University Press
%T Pseudo-Spectral Methods Applied to Gravitational Collapse
%B Frontiers in Numerical Relativity
%C Cambridge, U.K.; New York, U.S.A.
%E Evans, C.R. and Finn, L.S. and Hobill, D.W.
%D 1989
%P 239?253
%K Quadrupole formula

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/275
%A Bonazzola, S.
%A Frieben, J.
%A Gourgoulhon, E.
%A Marck, J.-A.
%S Proceedings of the Third International Conference on Spectral and High Order Methods: Houston, Texas, June 5 ? 9, 1995
%I University of Houston
%T Spectral methods in general relativity ? toward the simulation of 3D-gravitational collapse of neutron stars
%B ICOSAHOM ?95
%C Houston, U.S.A.
%E Ilin, A.V. and Scott, L.R.
%D 1996
%P 3?19
%K Einstein-Maxwell equations
%K Relativistic astrophysics

%0 
%U http://relativity.livingreviews.org/refdb/record/7555
%A Bonazzola, S.
%A Gourgoulhon, E.
%A Marck, J.-A.
%R 10.1016/S0377-0427(99)00167-3
%T Spectral methods in general astrophysics
%V 109
%D 1999
%P 433?473
%J J. Comput. Appl. Math.
%K Initial boundary value problem
%K Astrophysics

%0 
%U http://relativity.livingreviews.org/refdb/record/12483
%A Booth, I.
%T Black hole boundaries
%V 83
%D 2005
%P 1073?1099
%R 10.1139/p05-063
%J Can. J. Phys.
%K Causal structure
%K Generic collapse

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12484
%A Boyd, J.P.
%D 2001
%7 2nd rev.
%C Mineola, NY
%T Chebyshev and Fourier Spectral Methods
%I Dover Publications
%K Differential equations
%K Mathematical methods

%0 Electronic Source
%U http://relativity.livingreviews.org/refdb/record/12485
%A Brankin, R.W.
%A Gladwell, I.
%A Shampine, L.F.
%U http://www.netlib.org/ode/rksuite/
%I Dept. of Mathematics, Southern Methodist University, Dallas, TX
%9 other
%D 1992
%T RKSUITE: A Suite of Runge?Kutta Codes for the Initial Value Problem for ODEs

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12486
%A Brent, R.P.
%I Dover Publications
%D 2002
%C Mineola, U.S.A.
%T Algorithms for Minimization Without Derivatives

%0 
%U http://relativity.livingreviews.org/refdb/record/12487
%A Brewin, L.C.
%T Is the Regge Calculus a Consistent Approximation to General Relativity?
%V 32
%D 2000
%P 897?918
%R 10.1023/A:1001937108480
%J Gen. Relativ. Gravit.
%K Regge calculus

%0 
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%A Brewin, L.C.
%A Gentle, A.P.
%T On the Convergence of Regge Calculus to General Relativity
%V 18
%D 2001
%P 517?525
%R 10.1088/0264-9381/18/3/311
%J Class. Quantum Grav.

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12489
%A Briggs, W.L.
%A Henson, V.E.
%A McCormick, S.F.
%I SIAM
%C Philadelphia, U.S.A.
%7 2nd
%D 2000
%T A Multigrid Tutorial

%0 
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%A Brill, D.R.
%A Lindquist, R.W.
%R 10.1103/PhysRev.131.471
%T Interaction Energy in Geometrostatics
%V 131
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%P 471?476
%J Phys. Rev.
%K Black hole binaries

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%V 83
%D 1974
%P 449?457
%J Ann. Phys. (N.Y.)

%0 Electronic Source
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%A Schnetter, E.
%U http://www.carpetcode.org
%I Center for Computation and Technology, Louisiana State University
%9 project homepage
%T CarpetCode: A mesh refinement driver for Cactus
%K Scientific codes
%K Adaptive mesh refinement (AMR)

%0 Thesis
%U http://relativity.livingreviews.org/refdb/record/12492
%A Caveny, S.A.
%9 phd
%I University of Texas at Austin
%D 2002
%C Austin, U.S.A.
%T Tracking Black Holes in Numerical Relativity: Foundations and Applications
%K Topology change

%0 
%U http://relativity.livingreviews.org/refdb/record/12493
%A Caveny, S.A.
%A Anderson, M.
%A Matzner, R.A.
%T Tracking Black Holes in Numerical Relativity
%V 68
%D 2003
%P 104009
%J Phys. Rev. D

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%A Caveny, S.A.
%A Matzner, R.A.
%M 104003
%R 10.1103/PhysRevD.68.104003
%T Adaptive event horizon tracking and critical phenomena in binary black hole coalescence
%P 1?13
%V 68
%D 2003
%J Phys. Rev. D
%K Critical phenomena

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%A Choptuik, M.W.
%9 phd
%I University of British Columbia
%D 1986
%C Vancouver, Canada
%T A Study of Numerical Techniques for Radiative Problems in General Relativity
%K Mass functions

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/12496
%A Choptuik, M.W.
%S Proceedings of the International Workshop on Numerical Relativity, University of Illinois at Urbana-Champaign (Urbana-Champaign, Illinois, USA), May 9 ? 13, 1988
%I Cambridge University Press
%T Experiences with an Adaptive Mesh Refinement Algorithm in Numerical Relativity
%B Frontiers in Numerical Relativity
%C Cambridge, U.K.; New York, U.S.A.
%E Evans, C.R. and Finn, L.S. and Hobill, D.W.
%D 1989
%P 206?221

%0 
%U http://relativity.livingreviews.org/refdb/record/3783
%A Chru?ciel, P.T.
%A Galloway, G.J.
%T Horizons Non-Differentiable on a Dense Set
%V 193
%D 1998
%P 449?470
%J Commun. Math. Phys.
%K Global methods
%K Rigidity theorem
%K Horizon geometry

%0 Thesis
%U http://relativity.livingreviews.org/refdb/record/12497
%A Cook, G.B.
%9 phd
%I University of North Carolina at Chapel Hill
%D 1990
%C Chapel Hill, U.S.A.
%T Initial Data for the Two-Body Problem of General Relativity

%0 
%U http://relativity.livingreviews.org/refdb/record/12498
%A Cook, G.B.
%A York Jr, J.W.
%T Apparent Horizons for Boosted or Spinning Black Holes
%V 41
%D 1990
%P 1077?1085
%J Phys. Rev. D

%0 
%U http://relativity.livingreviews.org/refdb/record/4577
%A Cook, G.B.
%A Abrahams, A.M.
%T Horizon Structure of Initial-Data Sets for Axisymmetric Two-Black-Hole Collisions
%V 46
%D 1992
%P 702?713
%J Phys. Rev. D
%K Perturbation methods

%0 
%U http://relativity.livingreviews.org/refdb/record/12499
%A Curtis, A.R.
%A Reid, J.K.
%T The Choice of Step Lengths When Using Differences to Approximate Jacobian Matrices
%V 13
%D 1974
%P 121?126
%J J. Inst. Math. Appl.

%0 
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%A Davis, T.A.
%R 10.1145/992200.992205
%T A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
%V 30
%D 2004
%P 165?195
%J ACM Trans. Math. Software

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%A Davis, T.A.
%R 10.1145/992200.992206
%T Algorithm 832: UMFPACK V4.3?an unsymmetric-pattern multifrontal method
%V 30
%D 2004
%P 196?199
%J ACM Trans. Math. Software

%0 
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%A Davis, T.A.
%A Duff, I.S.
%T An unsymmetric-pattern multifrontal method for sparse LU factorization
%V 18
%D 1997
%P 140?158
%R 10.1137/S0895479894246905
%J SIAM J. Matrix Anal. Appl.

%0 
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%A Davis, T.A.
%A Duff, I.S.
%T A combined unifrontal/multifrontal method for unsymmetric sparse matrices
%V 25
%D 1999
%P 1?19
%R 10.1145/305658.287640
%J ACM Trans. Math. Software

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%U http://relativity.livingreviews.org/refdb/record/12504
%A Dennis Jr, J.E.
%A Schnabel, R.B.
%I SIAM
%D 1996
%C Philadelphia, U.S.A.
%T Numerical Methods for Unconstrained Optimization and Nonlinear Equations

%0 
%U http://relativity.livingreviews.org/refdb/record/12505
%A Diener, P.
%T A New General Purpose Event Horizon Finder for 3D
%V 20
%D 2003
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%R 10.1088/0264-9381/20/22/014
%J Class. Quantum Grav.

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%U http://relativity.livingreviews.org/refdb/record/12506
%A Diener, P.
%A Herrmann, F.
%A Pollney, D.
%A Schnetter, E.
%A Seidel, E.
%A Takahashi, R.
%A Thornburg, J.
%A Ventrella, J.
%T Accurate Evolution of Orbiting Binary Black Holes
%V 96
%D 2006
%P 121101
%R 10.1103/PhysRevLett.96.121101
%J Phys. Rev. Lett.

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%U http://relativity.livingreviews.org/refdb/record/12507
%A Diener, P.
%9 personal communication
%D 2007

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%A Dreyer, O.
%A Krishnan, B.
%A Shoemaker, D.
%A Schnetter, E.
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%R 10.1103/PhysRevD.67.024018
%T Introduction to isolated horizon in numerical relativity
%V 67
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%J Phys. Rev. D
%K Quasi-local quantities
%K Quasi-local angular momentum
%K Quasi-local mass

%0 Book
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%A Duff, I.S.
%A Erisman, A.M.
%A Reid, J.K.
%I Oxford University Press
%D 1986
%C Oxford, U.K.; New York, U.S.A.
%T Direct Methods for Sparse Matrices

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%A Frankel, S.P.
%P 135?152
%T Stability Conditions in the Numerical Treatment of Parabolic Differential Equations
%V 7
%D 1953
%J Math. Tables Aids Comput.
%K Parabolic equations

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%U http://relativity.livingreviews.org/refdb/record/12510
%A Dykema, P.G.
%9 phd
%I University of Texas at Austin
%D 1980
%C Austin, U.S.A.
%T The Numerical Simulation of Axially Symmetric Gravitational Collapse

%0 
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%A Eardley, D.M.
%T Gravitational Collapse of Marginally Bound Spheroids: Initial Conditions
%V 12
%D 1975
%P 3072?3076
%J Phys. Rev. D
%K Dust

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%U http://relativity.livingreviews.org/refdb/record/12512
%A Eppley, K.R.
%9 phd
%I Princeton University
%D 1975
%C Princeton, U.S.A.
%T The numerical evolution of the collision of two black holes
%K Foliations

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%U http://relativity.livingreviews.org/refdb/record/12513
%A Eppley, K.R.
%T Evolution of time-symmetric gravitational waves: Initial data and apparent horizons
%V 16
%D 1977
%P 1609?1614
%J Phys. Rev. D
%K Scalar curvature

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%U http://relativity.livingreviews.org/refdb/record/12514
%A Fornberg, B.
%D 1998
%C Cambridge; New York
%T A Practical Guide to Pseudospectral Methods
%I Cambridge University Press
%K Pseudospectral methods

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12515
%A Forsythe, G.E.
%A Malcolm, M.A.
%A Moler, C.B.
%I Prentice-Hall
%D 1977
%C Englewood Cliffs, U.S.A.
%T Computer Methods for Mathematical Computations

%0 
%U http://relativity.livingreviews.org/refdb/record/1711
%A Gentle, A.P.
%A Miller, W.A.
%R 10.1088/0264-9381/15/2/013
%T A fully (3+1)-dimensional Regge calculus model of the Kasner cosmology
%V 15
%D 1965
%P 389?405
%J Class. Quantum Grav.
%K Numerical cosmology
%K Cosmological models
%K Modes of instability
%K Accretion disks

%0 
%U http://relativity.livingreviews.org/refdb/record/12516
%A Gentle, A.P.
%T Regge Calculus: A Unique Tool for Numerical Relativity
%V 34
%D 2002
%P 1701?1718
%R 10.1023/A:1020128425143
%J Gen. Relativ. Gravit.

%0 
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%A Grayson, M.A.
%T The Heat Equation Shrinks Embedded Plane Curves to Round Points
%V 26
%D 1987
%P 285?314
%J J. Differ. Geom.

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/12518
%A Goodale, T.
%A Allen, G.
%A Lanfermann, G.
%A Massó, J.
%A Radke, T.
%A Seidel, E.
%A Shalf, J.
%S 5th International Conference, Porto, Portugal, June 26 ? 28, 2002: Selected papers and invited talks
%I Springer
%T The Cactus Framework and Toolkit: Design and Applications
%B High Performance Computing for Computational Science (VECPAR 2002)
%C Berlin, Germany; New York, U.S.A.
%V 2565
%E Palma, J.M.L.M.and Dongarra, J. and Hernández, V. and Sousa, A.A.
%D 2003
%P 197?227

%0 Book
%U http://relativity.livingreviews.org/refdb/record/7675
%A Gottlieb, D.
%A Orszag, S.A.
%I SIAM
%T Numerical Analysis of Spectral Methods: Theory and Applications
%C Philadelphia
%V 26
%D 1977

%0 
%U http://relativity.livingreviews.org/refdb/record/4615
%A Grandclément, P.
%A Bonazzola, S.
%A Gourgoulhon, E.
%A Marck, J.-A.
%R 10.1006/jcph.2001.6734
%T A multidomain spectral method for scalar and vectorial poisson equations with noncompact sources
%V 170
%D 2001
%P 231?260
%J J. Comput. Phys.
%K Helical Killing vectors
%K Numerical analysis

%0 
%U http://relativity.livingreviews.org/refdb/record/4175
%A Grandclément, P.
%A Gourgoulhon, E.
%A Bonazzola, S.
%M 044021
%R 10.1103/PhysRevD.65.044021
%T Binary black holes in circular orbits. II. Numerical methods and first results
%P 1?18
%V 65
%D 2002
%J Phys. Rev. D
%K Compact binaries

%0 
%U http://relativity.livingreviews.org/refdb/record/12519
%A Gundlach, C.
%T Pseudo-spectral apparent horizon finders: An efficient new algorithm
%V 57
%D 1998
%P 863?875
%J Phys. Rev. D

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/4072
%A Hawking, S.W.
%P 1?56
%D 1973
%E DeWitt, C.M. and DeWitt, B.S.
%C New York
%B Black Holes
%T The Event Horizon
%I Gordon and Breach
%S Based on lectures given at the 23rd session of the Summer School of Les Houches, 1972

%0 Book
%U http://relativity.livingreviews.org/refdb/record/1733
%A Hawking, S.W.
%A Ellis, G.F.R.
%D 1973
%C Cambridge
%T The Large Scale Structure of Space-Time
%I Cambridge University Press
%K Mathematical relativity
%K Gravity
%K Large scale structure
%K Cosmology
%K Singularity theorems
%K Hyperbolic symmetry
%K Cosmological spacetimes

%0 
%U http://relativity.livingreviews.org/refdb/record/4094
%A Hayward, S.A.
%P 6467?6474
%D 1994
%V 49
%T General laws of black-hole dynamics
%R 10.1103/PhysRevD.49.6467
%J Phys. Rev. D

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/12520
%A Hindmarsh, A.C.
%S Based on papers presented at the Tenth IMACS World Congress on System Simulation and Scientific Computation, held in Montreal, Canada, August 8 ? 13, 1982
%I North-Holland
%T ODEPACK, A Systematized Collection of ODE Solvers
%B Scientific Computing: Applications of Mathematics and Computing to the Physical Sciences
%C Amsterdam, Netherlands; New York, U.S.A.
%V 1
%E Stepleman, R.S. et al.
%D 1983
%P 55?64

%0 
%U http://relativity.livingreviews.org/refdb/record/12521
%A Hochbruck, M.
%A Lubich, C.
%A Selhofer, H.
%T Exponential Integrators for Large Systems of Differential Equations
%V 19
%D 1998
%P 1552?1574
%R 10.1137/S1064827595295337
%J SIAM J. Sci. Comput.

%0 
%U http://relativity.livingreviews.org/refdb/record/12522
%A Hornung, R.D.
%A Kohn, S.R.
%R 10.1002/cpe.652
%T Managing application complexity in the SAMRAI object-oriented framework
%V 14
%D 2002
%P 347?368
%J Concurr. Comput. Pract. Exp.

%0 
%U http://relativity.livingreviews.org/refdb/record/12523
%A Hornung, R.D.
%A Wissink, A.M.
%A Kohn, S.R.
%R 10.1007/s00366-006-0038-6
%T Managing complex data and geometry in parallel structured AMR applications
%V 22
%D 2006
%P 181?195
%J Eng. Comput.

%0 
%U http://relativity.livingreviews.org/refdb/record/4107
%A Hughes, S.A.
%A Keeton II, C.R.
%A Walker, P.
%A Walsh, K.T.
%A Shapiro, S.L.
%A Teukolsky, S.A.
%T Finding Black Holes in Numerical Spacetimes
%V 49
%D 1994
%P 4004?4015
%J Phys. Rev. D
%K Geodesics

%0 Thesis
%U http://relativity.livingreviews.org/refdb/record/12524
%A Huq, M.F.
%9 phd
%I The University of Texas at Austin
%D 1996
%C Austin, U.S.A.
%T Apparent Horizon Location in Numerical Spacetimes

%0 
%U http://relativity.livingreviews.org/refdb/record/12525
%A Huq, M.F.
%A Choptuik, M.W.
%A Matzner, R.A.
%M 084024
%T Locating Boosted Kerr and Schwarzschild Apparent Horizons
%V 66
%D 2002
%J Phys. Rev. D

%0 
%U http://relativity.livingreviews.org/refdb/record/2221
%A Husa, S.
%A Winicour, J.
%M 084019
%R 10.1103/PhysRevD.60.084019
%T Asymmetric merger of black holes
%V 60
%D 1999
%J Phys. Rev. D

%0 
%U http://relativity.livingreviews.org/refdb/record/12526
%A Gourgoulhon, E.
%A Jaramillo, J.L.
%R 10.1016/j.physrep.2005.10.005
%T A 3+1 perspective on null hypersurfaces and isolated horizons
%V 423
%D 2006
%P 159?294
%J Phys. Rep.

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12527
%A Kahaner, D.
%A Moler, C.B.
%A Nash, S.
%I Prentice Hall
%D 1989
%C Englewood Cliffs, U.S.A.
%T Numerical Methods and Software

%0 
%U http://relativity.livingreviews.org/refdb/record/12528
%A Kemball, A.J.
%A Bishop, N.T.
%T The numerical determination of apparent horizons
%V 8
%D 1991
%P 1361?1367
%R 10.1088/0264-9381/8/7/012
%J Class. Quantum Grav.

%0 
%U http://relativity.livingreviews.org/refdb/record/12529
%A Kershaw, D.S.
%T The Incomplete Cholesky-Conjugate Gradient Method for Interative Solution of Linear Equations
%V 26
%D 1978
%P 43?65
%R 10.1016/0021-9991(78)90098-0
%J J. Comput. Phys.

%0 
%U http://relativity.livingreviews.org/refdb/record/12530
%A Kidder, L.E.
%A Finn, L.S.
%M 084026
%R 10.1103/PhysRevD.62.084026
%T Spectral methods for numerical relativity: The initial data problem
%P 1?13
%V 62
%D 2000
%J Phys. Rev. D

%0 
%U http://relativity.livingreviews.org/refdb/record/12531
%A Kidder, L.E.
%A Scheel, M.A.
%A Teukolsky, S.A.
%A Carlson, E.D.
%A Cook, G.B.
%M 084032
%D 2000
%V 62
%T Black hole evolution by spectral methods
%R 10.1103/PhysRevD.62.084032
%J Phys. Rev. D
%K Hyperbolic partial differential equations

%0 Unpublished Work
%U http://relativity.livingreviews.org/refdb/record/12532
%A Kidder, L.E.
%A Scheel, M.A.
%A Teukolsky, S.A.
%A Cook, G.B.
%S Miniprogram on Colliding Black Holes: Mathematical Issues in Numerical Relativity, held at the Institute for Theoretical Physics, UC at Santa Barbara, 10 ? 28 January 2000
%9 conference paper
%D 2000
%T Spectral Evolution of Einstein?s Equations

%0 
%U http://relativity.livingreviews.org/refdb/record/12533
%A Kriele, M.
%A Hayward, S.A.
%T Outer trapped surfaces and their apparent horizon
%V 38
%D 1997
%P 1593?1604
%R 10.1063/1.532010
%J J. Math. Phys.

%0 
%U http://relativity.livingreviews.org/refdb/record/2220
%A Lehner, L.
%A Bishop, N.T.
%A Gómez, R.
%A Szilágyi, B.
%A Winicour, J.
%M 044005
%R 10.1103/PhysRevD.60.044005
%T Exact solutions for the intrinsic geometry of black hole coalescence
%V 60
%D 1999
%J Phys. Rev. D

%0 Electronic Source
%U http://relativity.livingreviews.org/refdb/record/9884
%A Lehner, L.
%A Gómez, R.
%A Husa, S.
%A Szilágyi, B.
%A Bishop, N.T.
%A Winicour, J.
%U http://www.psc.edu/research/graphics/gallery/winicour.html
%I Pittsburgh Supercomputing Center
%9 institutional homepage
%T Bagels Form When Black Holes Collide

%0 
%U http://relativity.livingreviews.org/refdb/record/12534
%A Leiler, G.
%A Rezzolla, L.
%M 044001
%T On the iterated Crank?Nicolson method for hyperbolic and parabolic equations in numerical relativity
%V 73
%D 2006
%J Phys. Rev. D

%0 
%U http://relativity.livingreviews.org/refdb/record/1766
%A Libson, J.
%A Massó, J.
%A Seidel, E.
%A Suen, W.-M.
%A Walker, P.
%T Event horizons in numerical relativity: Methods and tests
%V 53
%D 1996
%P 4335?4350
%J Phys. Rev. D

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/12535
%A Libson, J.
%A Massó, J.
%A Seidel, E.
%A Suen, W.-M.
%S Proceedings of the meeting held at Stanford University, July 24 ? 30, 1994
%I World Scientific
%T A 3D Apparent Horizon Finder
%B The Seventh Marcel Grossmann Meeting: On recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories
%C Singapore; River Edge, U.S.A.
%E Jantzen, R.T. and Keiser, G.M.
%D 1996
%P 631

%0 Personal Communication
%U http://relativity.livingreviews.org/refdb/record/12536
%A Lin, L.-M.
%A Novak, J.
%9 personal communication
%D 2006
%T Three-dimensional apparent horizon finder in LORENE

%0 
%U http://relativity.livingreviews.org/refdb/record/12537
%A Lorensen, W.E.
%A Cline, H.E.
%R 10.1145/37402.37422
%T Marching cubes: A high resolution 3D surface construction algorithm
%V 21
%D 1987
%P 163?169
%J SIGGRAPH Comput. Graph.

%0 Generic
%U http://relativity.livingreviews.org/refdb/record/12538
%A Madderom, P.
%9 unknown
%D 1984
%T Incomplete LU-Decomposition ? Conjugate Gradient

%0 
%U http://relativity.livingreviews.org/refdb/record/12539
%A MacNeice, P.
%A Olson, K.M.
%A Mobarry, C.
%A de Fainchtein, R.
%A Packer, C.
%T PARAMESH: A parallel adaptive mesh refinement community toolkit
%V 126
%D 2000
%P 330?354
%R 10.1016/S0010-4655(99)00501-9
%J Comput. Phys. Commun.

%0 
%U http://relativity.livingreviews.org/refdb/record/2240
%A Matzner, R.A.
%A Seidel, E.
%A Shapiro, S.L.
%A Smarr, L.L.
%A Suen, W.-M.
%A Teukolsky, S.A.
%A Winicour, J.
%R 10.1126/science.270.5238.941
%T Geometry of a Black Hole Collision
%V 270
%D 1995
%P 941?947
%J Science

%0 
%U http://relativity.livingreviews.org/refdb/record/12540
%A Metzger, J.
%T Numerical computation of constant mean curvature surfaces using finite elements
%V 21
%D 2004
%P 4625?4646
%R 10.1088/0264-9381/21/19/010
%J Class. Quantum Grav.

%0 
%U http://relativity.livingreviews.org/refdb/record/12541
%A Miller, M.A.
%T Regge Calculus as a Fourth Order Method in Numerical Relativity
%V 12
%D 1995
%P 3037?3051
%R 10.1088/0264-9381/12/12/019
%J Class. Quantum Grav.

%0 
%U http://relativity.livingreviews.org/refdb/record/7331
%A Misner, C.W.
%A Sharp, D.H.
%P B571?B576
%D 1964
%V 136
%T Relativistic equations for adiabatic, spherically symmetric gravitational collapse
%R 10.1103/PhysRev.136.B571
%J Phys. Rev.
%K Thermodynamics
%K Supernovae

%0 Book
%U http://relativity.livingreviews.org/refdb/record/96
%A Misner, C.W.
%A Thorne, K.S.
%A Wheeler, J.A.
%T Gravitation
%C San Francisco
%D 1973
%I W.H. Freeman
%K Special relativity
%K Exact solutions
%K Kerr-Newman metric
%K Gravitational radiation
%K Analysis
%K Gravitational waves
%K Spacetime formalism
%K Spinors
%K Gravitational wave detectors
%K Tensor analysis
%K Differential geometry
%K Fundamental physics
%K Theories of gravity
%K Newtonian stars
%K Stability theory

%0 
%U http://relativity.livingreviews.org/refdb/record/12542
%A Nakamura, T.
%A Kojima, Y.
%A Oohara, K.
%R 10.1016/0375-9601(84)91016-8
%T A method of determining apparent horizons in three-dimensional numerical relativity
%V 106
%D 1984
%P 235?238
%J Phys. Lett. A

%0 
%U http://relativity.livingreviews.org/refdb/record/12543
%A Oohara, K.
%A Nakamura, T.
%A Kojima, Y.
%T Apparent Horizons of Time-Symmetric Initial Value for Three Black Holes
%V 107
%D 1985
%P 452?455
%R 10.1016/0375-9601(85)90423-2
%J Phys. Lett. A

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/12544
%A Oohara, K.
%S Proceedings of Yamada Conference XIV, Kyoto International Conference Hall, Japan, April 7 ? 11, 1986
%I World Scientific
%T Apparent Horizon of Initial Data for Black Hole-Collisions
%B Gravitational Collapse and Relativity
%C Singapore; Philadelphia, U.S.A.
%E Sato, H. and Nakamura, T.
%D 1986
%P 313?319

%0 
%U http://relativity.livingreviews.org/refdb/record/12545
%A Osher, S.
%A Sethian, J.A.
%T Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton?Jacobi formulations
%V 79
%D 1988
%P 12?49
%R 10.1016/0021-9991(88)90002-2
%J J. Comput. Phys.

%0 Book Section
%U http://relativity.livingreviews.org/refdb/record/12546
%A Parashar, M.
%A Browne, J.C.
%I Springer
%T System Engineering for High Performance Computing Software: The {HDDA}/{DAGH} Infrastructure for Implementation of Parallel Structured Adaptive Mesh Refinement
%B Structured Adaptive Mesh Refinement (SAMR) Grid Methods
%C New York, U.S.A.
%V 117
%E Baden, S.B. and Chrisochoides, N.P. and Gannon, D.B. and Norman, M.L.
%D 2000
%P 1?18

%0 Report
%U http://relativity.livingreviews.org/refdb/record/12547
%A Pasch, E.
%N 63
%I University of Tübingen
%T The level set method for the mean curvature flow on (R^{3},g)
%U http://www.uni-tuebingen.de/uni/opx/reports.html
%C Tübingen, Germany
%D 1997

%0 
%U http://relativity.livingreviews.org/refdb/record/12548
%A Petrich, L.I.
%A Shapiro, S.L.
%A Teukolsky, S.A.
%T Oppenheimer?Snyder Collapse with Maximal Time Slicing and Isotropic Coordinates
%V 31
%D 1985
%P 2459?2469
%J Phys. Rev. D

%0 Electronic Source
%U http://relativity.livingreviews.org/refdb/record/12549
%A Balay, S.
%A Buschelman, K.
%A Gropp, W.D.
%A Kaushik, D.
%A Knepley, M.
%A Curfman McInnes, L.
%A Smith, B.F.
%A Zhang, H.
%U http://www.mcs.anl.gov/petsc
%I Argonne National Laboratory
%9 project homepage
%T PETSc: Portable, Extensible Toolkit for Scientific Computation

%0 Report
%U http://relativity.livingreviews.org/refdb/record/12550
%A Balay, S.
%A Buschelman, K.
%A Gropp, W.D.
%A Kaushik, D.
%A Knepley, M.
%A Curfman McInnes, L.
%A Smith, B.F.
%A Zhang, H.
%N ANL-95/11 ? Revision 2.1.5
%I Argonne National Laboratory
%T PETSc Users Manual
%U http://www-unix.mcs.anl.gov/petsc/petsc-as/documentation/
%C Argonne, U.S.A.
%D 2003

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/12551
%A Balay, S.
%A Gropp, W.D.
%A Curfman McInnes, L.
%A Smith, B.F.
%S Proceedings of SciTools ?96 Workshop held in Oslo, Norway
%I Birkhäuser
%T Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries
%B Modern Software Tools for Scientific Computing
%C Boston, U.S.A.
%E Arge, E. and Bruaset, A.M. and Langtangen, H.P.
%D 1997
%P 163?202

%0 Thesis
%U http://relativity.livingreviews.org/refdb/record/12552
%A Pfeiffer, H.P.
%9 phd
%I Cornell University
%D 2003
%C Ithaca, U.S.A.
%T Initial Data for Black Hole Evolutions

%0 
%U http://relativity.livingreviews.org/refdb/record/4170
%A Pfeiffer, H.P.
%A Teukolsky, S.A.
%A Cook, G.B.
%M 104018
%R 10.1103/PhysRevD.62.104018
%T Quasicircular orbits for spinning binary black holes
%V 62
%D 2000
%J Phys. Rev. D
%K Binary black holes
%K Spinning binary black holes

%0 
%U http://relativity.livingreviews.org/refdb/record/12553
%A Pfeiffer, H.P.
%A Kidder, L.E.
%A Scheel, M.A.
%A Teukolsky, S.A.
%R 10.1016/S0010-4655(02)00847-0
%T A multidomain spectral method for solving elliptic equations
%V 152
%D 2003
%P 253?273
%J Comput. Phys. Commun.

%0 
%U http://relativity.livingreviews.org/refdb/record/4171
%A Pfeiffer, H.P.
%A Cook, G.B.
%A Teukolsky, S.A.
%M 024047
%R 10.1103/PhysRevD.66.024047
%T Comparing initial-data sets for binary black holes
%P 1?17
%V 66
%D 2002
%J Phys. Rev. D

%0 Personal Communication
%U http://relativity.livingreviews.org/refdb/record/12554
%A Pfeiffer, H.P.
%9 personal communication
%D 2006

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12555
%A Press, W.H.
%A Flannery, B.P.
%A Teukolsky, S.A.
%A Vetterling, W.T.
%I Cambridge University Press
%C Cambridge, U.K.; New York, U.S.A.
%7 2nd
%D 1992
%T Numerical Recipes

%0 
%U http://relativity.livingreviews.org/refdb/record/9898
%A Pretorius, F.
%A Lehner, L.
%R 10.1016/j.jcp.2004.01.001
%T Adaptive mesh refinement for characteristic codes
%V 198
%D 2004
%P 10?34
%J J. Comput. Phys.

%0 
%U http://relativity.livingreviews.org/refdb/record/12556
%A Pretorius, F.
%A Choptuik, M.W.
%P 246?274
%D 2006
%V 218
%T Adaptive mesh refinement for coupled elliptic-hyperbolic systems
%R 10.1016/j.jcp.2006.02.011
%J J. Comput. Phys.
%K Domain decomposition

%0 
%U http://relativity.livingreviews.org/refdb/record/2597
%A Regge, T.
%T General Relativity without Coordinates
%V 19
%D 1961
%P 558?571
%J Nuovo Cimento A

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12557
%A Richtmyer, R.D.
%A Morton, K.W.
%I Krieger
%C Malabar, U.S.A.
%7 2nd
%D 1994
%T Difference Methods for Initial-Value Problems

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12558
%A Saad, Y.
%I SIAM
%C Philadelphia, U.S.A.
%7 2nd
%D 2003
%T Iterative Methods for Sparse Linear Systems

%0 Electronic Source
%U http://relativity.livingreviews.org/refdb/record/12559
%A Schnetter, E.
%U http://arXiv.org/abs/gr-qc/0206003
%9 arxiv
%D 2002
%T A fast apparent horizon algorithm

%0 
%U http://relativity.livingreviews.org/refdb/record/12560
%A Schnetter, E.
%T Finding Apparent Horizons and other Two-Surfaces of Constant Expansion
%V 20
%D 2003
%P 4719?4737
%R 10.1088/0264-9381/20/22/001
%J Class. Quantum Grav.

%0 
%U http://relativity.livingreviews.org/refdb/record/12561
%A Schnetter, E.
%A Hawley, S.H.
%A Hawke, I.
%P 1465?1488
%D 2004
%V 21
%T Evolutions in 3-D numerical relativity using fixed mesh refinement
%R 10.1088/0264-9381/21/6/014
%J Class. Quantum Grav.

%0 
%U http://relativity.livingreviews.org/refdb/record/12562
%A Schnetter, E.
%A Herrmann, F.
%A Pollney, D.
%M 044033
%T Horizon Pretracking
%V 71
%D 2005
%J Phys. Rev. D

%0 
%U http://relativity.livingreviews.org/refdb/record/12563
%A Schnetter, E.
%A Krishnan, B.
%M 021502
%T Nonsymmetric trapped surfaces in the Schwarzschild Vaidya spacetimes
%V 73
%D 2006
%J Phys. Rev. D
%K Vaidya spacetime

%0 
%U http://relativity.livingreviews.org/refdb/record/12564
%A Schnetter, E.
%A Krishnan, B.
%A Beyer, F.
%M 024028
%T Introduction to Dynamical Horizons in numerical relativity
%V 74
%D 2006
%J Phys. Rev. D
%K Multipole expansions
%K Quasi-local energy-momentum

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12565
%A Schroeder, M.R.
%I Springer
%T Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity
%C Berlin, Germany; New York, U.S.A.
%V 7
%7 2nd
%D 1986

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%A Seidel, E.
%A Suen, W.-M.
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%A Shampine, L.F.
%A Gordon, M.K.
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%T Computer solution of Ordinary Differential Equations

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%A Shapiro, S.L.
%A Teukolsky, S.A.
%R 10.1086/183134
%T Gravitational Collapse of Supermassive Stars to Black Holes: Numerical Solution of the Einstein Equations
%V 234
%D 1979
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%J Astrophys. J. Lett.
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%T Relativistic stellar dynamics on the computer. I. Motivation and Numerical Method
%V 298
%D 1985
%P 34?57
%R 10.1086/163587
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%A Shapiro, S.L.
%A Teukolsky, S.A.
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%V 298
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%P 58?79
%J Astrophys. J.
%K Vlasov equation
%K Stellar dynamics
%K Einstein-Vlasov system
%K Kinetic theory
%K Stability

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%A Shapiro, S.L.
%A Teukolsky, S.A.
%T Collision of relativistic clusters and the formation of black holes
%V 45
%D 1992
%P 2739?2750
%J Phys. Rev. D

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%T Apparent horizon finder for a special family of spacetimes in 3D numerical relativity
%V 55
%D 1997
%P 2002?2013
%J Phys. Rev. D

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%A Shibata, M.
%A Ury?, K.
%M 087501
%T Apparent Horizon Finder for General Three-Dimensional Spaces
%V 62
%D 2000
%J Phys. Rev. D

%0 Thesis
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%A Shoemaker, D.M.
%9 phd
%I The University of Texas at Austin
%D 1999
%C Austin, U.S.A.
%T Apparent Horizons in Binary Black Hole Spacetimes

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%U http://relativity.livingreviews.org/refdb/record/4194
%A Shoemaker, D.M.
%A Huq, M.F.
%A Matzner, R.A.
%M 124005
%T Generic tracking of multiple apparent horizons with level flow
%V 62
%D 2000
%J Phys. Rev. D

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%A Stoer, J.
%A Bulirsch, R.
%I Springer
%D 1980
%C Berlin, Germany; New York, U.S.A.
%T Introduction to Numerical Analysis

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%A Szilágyi, B.
%A Pollney, D.
%A Rezzolla, L.
%A Thornburg, J.
%A Winicour, J.
%P S275?S293
%D 2007
%V 24
%T An explicit harmonic code for black-hole evolution using excision
%R 10.1088/0264-9381/24/12/S18
%J Class. Quantum Grav.
%K Harmonic coordinates
%K Harmonic gauge
%K Wave equation

%0 
%U http://relativity.livingreviews.org/refdb/record/1816
%A Teukolsky, S.A.
%M 087501
%D 2000
%V 61
%T Stability of the iterated Crank-Nicholson method in numerical relativity
%R 10.1103/PhysRevD.61.087501
%J Phys. Rev. D
%K Numerical stability

%0 
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%A Thornburg, J.
%T Finding apparent horizons in numerical relativity
%V 54
%D 1996
%P 4899?4918
%J Phys. Rev. D

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%A Thornburg, J.
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%T A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes ? I: Initial Data
%V 59
%D 1999
%J Phys. Rev. D

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%A Thornburg, J.
%U http://arXiv.org/abs/gr-qc/9906022
%9 arxiv
%D 1999
%T A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes ? II: Time Evolution

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%U http://relativity.livingreviews.org/refdb/record/4195
%A Thornburg, J.
%R 10.1088/0264-9381/21/2/026
%T A fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity
%V 21
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%P 743?766
%J Class. Quantum Grav.

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%A Tod, K.P.
%T Looking for marginally trapped surfaces
%V 8
%D 1991
%P L115?L118
%J Class. Quantum Grav.

%0 Book
%U http://relativity.livingreviews.org/refdb/record/12578
%A Trottenberg, U.
%A Oosterlee, C.W.
%A Schüller, A.
%I Academic Press
%D 2001
%C San Diego, U.S.A.
%T Multigrid

%0 Electronic Source
%U http://relativity.livingreviews.org/refdb/record/12579
%A Davis, T.A.
%U http://www.cise.ufl.edu/research/sparse/umfpack/
%I University of Florida (CISE)
%9 project homepage
%T UMFPACK: unsymmetric multifrontal sparse LU factorization package

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%U http://relativity.livingreviews.org/refdb/record/845
%A Wald, R.M.
%D 1984
%C Chicago
%T General Relativity
%I University of Chicago Press
%K Hamiltonian general relativity
%K Equivalence principle
%K Quantum field theory in curved spacetime

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%A Wald, R.M.
%A Iyer, V.
%T Trapped surfaces in the Schwarzschild geometry and cosmic censorship
%V 44
%D 1991
%P R3719?R3722
%J Phys. Rev. D

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%U http://relativity.livingreviews.org/refdb/record/12580
%A Walker, P.
%9 phd
%I University of Illinois at Urbana-Champaign
%D 1998
%C Urbana, U.S.A.
%T Horizons, Hyperbolic Systems, and Inner Boundary Conditions in Numerical Relativity

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/2225
%A York Jr, J.W.
%P 83?126
%D 1979
%E Smarr, L.L.
%C Cambridge; New York
%B Sources of Gravitational Radiation
%T Kinematics and Dynamics of General Relativity
%I Cambridge University Press
%S Proceedings of the Battelle Seattle Workshop, July 24 ? August 4, 1978
%K Gauge conditions

%0 Conference Paper
%U http://relativity.livingreviews.org/refdb/record/4575
%A York Jr, J.W.
%S Proceedings of the International Workshop on Numerical Relativity, University of Illinois at Urbana-Champaign, U.S.A., May 9 ? 13, 1988
%I Cambridge University Press
%T Initial Data for Collisions of Black Holes and Other Gravitational Miscellany
%B Frontiers in Numerical Relativity
%C Cambridge, U.K.; New York, U.S.A.
%E Evans, C.R. and Finn, L.S. and Hobill, D.W.
%D 1989
%P 89?109