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@article{Abrahams92b,
author = {Abrahams, A. M. and Evans, C. R.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Gravitational collapse, Maximal slicing, Numerical relativity},
pages = {R4117--R4121},
title = {Trapping a Geon: Black Hole Formation by an Imploding Gravitational Wave},
volume = {46},
year = {1992}
}
@article{Abrahams92c,
author = {Abrahams, A. M. and Heiderich, K. H. and Shapiro, S. L. and Teukolsky, S. A.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Brill waves, Cosmic censorship, Curvature, Hoop conjecture, Multi black hole spacetimes, Numerical relativity, Prolate collapse},
pages = {2452--2463},
title = {Vacuum initial data, singularities, and cosmic censorship},
volume = {46},
year = {1992}
}
@article{Abrahams94a,
author = {Abrahams, A. M. and Cook, G. B. and Shapiro, S. L. and Teukolsky, S. A.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Angular momentum, Axial symmetry, Axisymmetric black holes, Black hole formation, Black holes, Collisionless matter, Distorted black holes, Event horizons, Finite difference methods, Gravitational collapse, Kerr black holes, Numerical relativity, Partial differential equations, Prolate collapse, Rotating black holes},
pages = {5153--5164},
title = {Solving Einstein's Equations for Rotating Spacetimes: Evolution of Relativistic Star Clusters},
volume = {49},
year = {1994}
}
@article{Alcubierre98b,
adsurl = {http://adsabs.harvard.edu/abs/2000CQGra..17.2159A},
author = {Alcubierre, M. and Brandt, S. and Br{\"{u}}gmann, B. and Gundlach, C. and Mass{\'{o}}, J. and Seidel, E. and Walker, P.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/17/11/301},
journal = {Class. Quantum Grav.},
keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Black holes, Distorted black holes, Finite difference methods, Minimization, Kerr black holes, Multi black hole solutions, Numerical methods, Numerical relativity, Ordinary differential equations, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/9809004},
pages = {2159--2190},
title = {Test-beds and applications for apparent horizon finders in numerical relativity},
volume = {17},
year = {2000}
}
@article{Alcubierre2003:pre-ISCO-coalescence-times,
author = {Alcubierre, M. and Br{\"{u}}gmann, B. and Diener, P. and Guzm{\'{a}}n, F. S. and Hawke, I. and Hawley, S. and Herrmann, F. and Koppitz, M. and Pollney, D. and Seidel, E. and Thornburg, J.},
cited = {9 January 2006},
eid = {044004},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black hole angular momentum, Black hole collisions, Black hole formation, Black holes, Distorted black holes, Event horizons, Excision, Finite difference methods, Multi black hole spacetimes, Numerical methods, Numerical relativity, Partial differential equations, Rotating black holes, Smarr formula, Vacuum Einstein equations, Innermost stable circular orbits (ISCO)},
onlineversion = {http://arXiv.org/abs/gr-qc/0411149},
title = {Dynamical evolution of quasi-circular binary black hole data},
volume = {72},
year = {2005}
}
@misc{Andersson-Metzger-2007:conditions-for-MOTS-to-intersect,
author = {Andersson, L. and Metzger, J.},
format = {personal communication},
keywords = {Apparent horizons, Trapped surfaces},
note = {Personal communication from Lars Andersson to Bela Szil\'{a}gyi},
year = {2007}
}
@article{Anninos94e,
adsurl = {http://adsabs.harvard.edu/abs/1995PhRvD..51.5562A},
archiveprefix = {arXiv},
author = {Anninos, P. and Daues, G. and Mass{\'{o}}, J. and Seidel, E. and Suen, W.-M.},
doi = {10.1103/PhysRevD.51.5562},
eprint = {gr-qc/9412069},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black holes, Boundary conditions, Excision, Numerical relativity},
pages = {5562--5578},
title = {Horizon boundary conditions for black hole spacetimes},
volume = {51},
year = {1995}
}
@article{Anninos94f,
author = {Anninos, P. and Bernstein, D. and Brandt, S. and Libson, J. and Mass{\'{o}}, J. and Seidel, E. and Smarr, L. L. and Suen, W.-M. and Walker, P.},
cited = {9 January 2006},
doi = {10.1103/PhysRevLett.74.630},
journal = {Phys. Rev. Lett.},
keywords = {Apparent horizons, Black holes, Distorted black holes, Event horizons, Multi black hole spacetimes, Null surfaces},
onlineversion = {http://arXiv.org/abs/gr-qc/9403011},
pages = {630--633},
title = {Dynamics of Apparent and Event Horizons},
volume = {74},
year = {1995}
}
@article{Anninos98b,
author = {Anninos, P. and Camarda, K. and Libson, J. and Mass{\'{o}}, J. and Seidel, E. and Suen, W.-M.},
eid = {024003},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Distorted black holes, Kerr black holes, Minimization, Multi black hole spacetimes, Numerical methods, Numerical relativity, Schwarzschild solution, Spectral methods},
pages = {1--12},
title = {Finding apparent horizons in dynamic 3D numerical spacetimes},
volume = {58},
year = {1998}
}
@article{Ansorg:2003br,
adsurl = {http://adsabs.harvard.edu/abs/2003A&A...405..711A},
author = {Ansorg, M. and Kleinw{\"{a}}chter, A. and Meinel, R.},
cited = {9 January 2006},
doi = {10.1051/0004-6361:20030618},
journal = {Astron. Astrophys.},
keywords = {Axial symmetry, Boundary value problems, Nonlinear algebraic equations, Numerical methods, Numerical relativity, Relativistic fluids, Rotating stars, Spectral methods, Stationary solutions},
onlineversion = {http://arXiv.org/abs/astro-ph/0301173},
pages = {711--721},
title = {Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods},
volume = {405},
year = {2003}
}
@article{Ansorg:2004ds,
adsurl = {http://adsabs.harvard.edu/abs/2004PhRvD..70f4011A},
author = {Ansorg, M. and Br{\"{u}}gmann, B. and Tichy, W.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.70.064011},
eid = {064011},
journal = {Phys. Rev. D},
keywords = {Boundary conditions, Boundary value problems, Elliptic equations, Linear equations, Nonlinear algebraic equations, Multi black hole solutions, Nonlinear equations, Numerical methods, Numerical relativity, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/0404056},
pages = {1--13},
title = {Single-domain spectral method for black hole puncture data},
volume = {70},
year = {2004}
}
@article{Ansorg:2005bp,
adsurl = {http://adsabs.harvard.edu/abs/2005PhRvD..72b4018A},
author = {Ansorg, M.},
cited = {30 January 2007},
doi = {10.1103/PhysRevD.72.024018},
eid = {024018},
journal = {Phys. Rev. D},
keywords = {Boundary conditions, Boundary value problems, Elliptic equations, Linear equations, Nonlinear algebraic equations, Multi black hole solutions, Numerical methods, Numerical relativity, Spectral methods},
onlineversion = {http://arxiv.org/abs/gr-qc/0505059},
pages = {1--10},
title = {Double-domain spectral method for black hole excision data},
volume = {72},
year = {2005}
}
@article{Ansorg05,
author = {Ansorg, M. and Petroff, D.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.72.024019},
eid = {024019},
eprint = {gr-qc/0505060},
journal = {Phys. Rev. D},
keywords = {Axial symmetry, Black holes, Boundary value problems, Event horizons, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity, Relativistic fluids, Rotating black holes, Spectral methods, Stationary solutions},
numpages = {12},
onlineversion = {http://arXiv.org/abs/gr-qc/0505060},
title = {Black holes surrounded by uniformly rotating rings},
volume = {72},
year = {2005}
}
@incollection{Arnowitt62,
address = {New York; London},
adsurl = {http://adsabs.harvard.edu/abs/2008GReGr..40.1997A},
archiveprefix = {arXiv},
author = {Arnowitt, R. and Deser, S. and Misner, C. W.},
booktitle = {Gravitation: An Introduction to Current Research},
cited = {9 January 2006},
doi = {10.1007/s10714-008-0661-1},
editor = {Witten, L.},
eprint = {gr-qc/0405109},
keywords = {ADM formalism, Cauchy problem, Constraint equations},
onlineversion = {http://arXiv.org/abs/gr-qc/0405109},
pages = {227--265},
primaryclass = {gr-qc},
publisher = {Wiley},
title = {The dynamics of general relativity},
year = {1962}
}
@book{Ascher-Mattheij-Russel-1988,
address = {Englewood Cliffs, U.S.A.},
author = {Ascher, U. M. and Mattheij, R. M. M. and Russell, R. D.},
keywords = {Boundary value problems, Finite difference methods, Nonlinear algebraic equations, Ordinary differential equations},
publisher = {Prentice-Hall},
title = {Numerical Solution of Boundary Value Problems for Ordinary Differential Equations},
year = {1988}
}
@article{Ashtekar98a,
archiveprefix = {arXiv},
author = {Ashtekar, A. and Beetle, C. and Fairhurst, S.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/16/2/027},
eprint = {gr-qc/9812065},
journal = {Class. Quantum Grav.},
keywords = {Boundary conditions, Dynamical horizons, Event horizons, Horizons, Null surfaces, Quasi-local black holes, Three-manifolds, Trapping horizons},
onlineversion = {http://arXiv.org/abs/gr-qc/9812065},
pages = {L1--L7},
primaryclass = {gr-qc},
title = {Isolated horizons: a generalization of black hole mechanics},
volume = {16},
year = {1999}
}
@article{Ashtekar-etal-2002-dynamical-horizons,
author = {Ashtekar, A. and Krishnan, B.},
cited = {9 January 2006},
doi = {10.1103/PhysRevLett.89.261101},
eid = {261101},
eprint = {gr-qc/0207080},
journal = {Phys. Rev. Lett.},
keywords = {Black holes, Constraint equations, Dynamical horizons, Event horizons, Hamiltonian constraint, Horizons, Killing field, Killing horizons, Null surfaces, Quasi-local black holes, Three-manifolds, Trapped surfaces, Trapping horizons},
onlineversion = {http://arXiv.org/abs/gr-qc/0207080},
title = {Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws},
volume = {89},
year = {2002}
}
@article{Ashtekar03a,
author = {Ashtekar, A. and Krishnan, B.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.68.104030},
eid = {104030},
eprint = {gr-qc/0308033},
journal = {Phys. Rev. D},
keywords = {Black holes, Constraint equations, Dynamical horizons, Event horizons, Hamiltonian constraint, Horizons, Killing field, Killing horizons, Null surfaces, Quasi-local black holes, Three-manifolds, Trapped surfaces, Trapping horizons},
numpages = {25},
onlineversion = {http://arXiv.org/abs/gr-qc/0308033},
title = {Dynamical horizons and their properties},
volume = {68},
year = {2003}
}
@article{Ashtekar05,
author = {Ashtekar, A. and Galloway, J. G.},
cited = {9 January 2006},
eprint = {gr-qc/0503109},
journal = {Adv. Theor. Math. Phys.},
keywords = {Apparent horizons, Area increase law, Black holes, Dynamical horizons, Event horizons, Horizons, Isolated horizons, Killing field, Null surfaces, Three-manifolds, Trapped surfaces, Trapping horizons},
onlineversion = {http://arXiv.org/abs/gr-qc/0503109},
pages = {1--30},
title = {Some uniqueness results for dynamical horizons},
volume = {95},
year = {2005}
}
@article{Ashtekar:2004cn,
archiveprefix = {arXiv},
author = {Ashtekar, A. and Krishnan, B.},
cited = {9 January 2006},
eid = {lrr-2004-10},
eprint = {gr-qc/0407042},
journal = {Living Rev. Relativity},
keywords = {Black holes, Constraint equations, Dynamical horizons, Event horizons, Hamiltonian constraint, Horizons, Killing field, Killing horizons, Null surfaces, Quasi-local black holes, Three-manifolds, Trapped surfaces, Trapping horizons},
title = {Isolated and Dynamical Horizons and Their Applications},
url = {http://www.livingreviews.org/lrr-2004-10},
volume = {7},
year = {2004}
}
@article{Baiotti04,
adsurl = {http://adsabs.harvard.edu/abs/2005PhRvD..71b4035B},
author = {Baiotti, L. and Hawke, I. and Montero, P. J. and L{\"{o}}ffler, F. and Rezzolla, L. and Stergioulas, N. and Font, J. A. and Seidel, E.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.71.024035},
eid = {024035},
eprint = {gr-qc/0403029},
journal = {Phys. Rev. D},
keywords = {Angular momentum, Apparent horizons, Black hole formation, Black holes, Computational fluid dynamics, Constraints, Distorted black holes, Event horizons, Excision, Finite difference methods, Finite volume methods, Gravitational collapse, Hamiltonian constraint, Horizons, Instability, Mass formula, Numerical methods, Numerical relativity, Relativistic fluid dynamics, Relativistic hydrodynamics, Rotating black holes, Rotating stars, Smarr formula, Trapped surfaces},
onlineversion = {http://arXiv.org/abs/gr-qc/0403029},
title = {Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole},
volume = {71},
year = {2005}
}
@misc{Bartnik-proof:mean-curvature-flow-cant-move-through-AH,
author = {Bartnik, R.},
format = {personal communication},
keywords = {Apparent horizons, Inverse mean curvature flow, Ricci flow},
note = {Personal communication from Robert Bartnik to Carsten Gundlach}
}
@article{Baumgarte96,
adsurl = {http://adsabs.harvard.edu/abs/1996PhRvD..54.4849B},
author = {Baumgarte, T. W. and Cook, G. B. and Scheel, M. A. and Shapiro, S. L. and Teukolsky, S. A.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.54.4849},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black holes, Minimization, Numerical methods, Numerical relativity, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/9606010},
pages = {4849--4857},
title = {Implementing an apparent-horizon finder in three dimensions},
volume = {54},
year = {1996}
}
@article{Baumgarte:2002jm,
adsurl = {http://adsabs.harvard.edu/abs/2003PhR...376...41B},
archiveprefix = {arXiv},
author = {Baumgarte, T. W. and Shapiro, S. L.},
cited = {9 January 2006},
doi = {10.1016/S0370-1573(02)00537-9},
eprint = {gr-qc/0211028},
journal = {Phys. Rep.},
keywords = {Apparent horizons, Black holes, Event horizons, Finite difference methods, Numerical methods, Numerical relativity, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/0211028},
pages = {41--131},
primaryclass = {gr-qc},
title = {Numerical relativity and compact binaries},
volume = {376},
year = {2003}
}
@techreport{Bernstein-1993:mean-curvature-flow,
address = {Urbana-Champaign, U.S.A.},
author = {Bernstein, D.},
keywords = {Apparent horizons, Finite difference methods, Inverse mean curvature flow, Numerical methods, Numerical relativity, Ricci flow},
month = {November},
publisher = {National Center for Supercomputing Applications},
title = {Notes on the Mean Curvature Flow Method for Finding Apparent Horizons},
year = {1993}
}
@article{Bishop82,
author = {Bishop, N. T.},
doi = {10.1007/BF00756083},
journal = {Gen. Relativ. Gravit.},
keywords = {Apparent horizons, Black holes, Horizons, Multi black hole solutions, Numerical relativity},
pages = {717--723},
title = {The Closed Trapped Region and the Apparent Horizon of Two Schwarzschild Black Holes},
volume = {14},
year = {1982}
}
@article{Bishop84,
author = {Bishop, N. T.},
journal = {Gen. Relativ. Gravit.},
keywords = {Apparent horizons, Black holes, Horizons, Multi black hole solutions, Numerical relativity, Ordinary differential equations},
pages = {589--593},
title = {The horizons of two Schwarzschild black holes},
volume = {16},
year = {1984}
}
@article{Bishop88,
author = {Bishop, N. T.},
doi = {10.1007/BF00758912},
journal = {Gen. Relativ. Gravit.},
keywords = {Approximation methods, Black holes, Event horizons},
pages = {573--581},
title = {The Event Horizons of Two Schwarzschild black holes},
volume = {20},
year = {1988}
}
@article{Bizon-Malec-OMurchadha-1988,
author = {Bizo{\'{n}}, P. and Malec, E. and {\'{O}} Murchadha, N.},
journal = {Phys. Rev. Lett.},
keywords = {Cosmic censorship, Maximal hypersurfaces, Hamiltonian constraint, Spherical symmetry, Trapped surfaces},
pages = {1147--1150},
title = {Trapped Surfaces in Spherical Stars},
volume = {61},
year = {1988}
}
@inproceedings{Bonazzola89,
address = {Cambridge, U.K.; New York, U.S.A.},
author = {Bonazzola, S. and Marck, J.-A.},
booktitle = {Frontiers in Numerical Relativity},
conference = {Proceedings of the International Workshop on Numerical Relativity, University of Illinois at Urbana-Champaign, USA, May 9\,--\,13, 1988},
editor = {Evans, C. R. and Finn, L. S. and Hobill, D. W.},
keywords = {Axial symmetry, Computational fluid dynamics, Gravitational collapse, Numerical methods, Quadrupole formula, Spectral methods, Spherical symmetry},
pages = {239--253},
publisher = {Cambridge University Press},
title = {Pseudo-Spectral Methods Applied to Gravitational Collapse},
year = {1989}
}
@inproceedings{Bonazzola-etal-1996:spectral-methods-in-gr,
address = {Houston, U.S.A.},
author = {Bonazzola, S. and Frieben, J. and Gourgoulhon, E. and Marck, J.-A.},
booktitle = {ICOSAHOM '95},
cited = {9 January 2006},
conference = {Proceedings of the Third International Conference on Spectral and High Order Methods: Houston, Texas, June 5\,--\,9, 1995},
editor = {Ilin, A. V. and Scott, L. R.},
keywords = {Computational fluid dynamics, Relativistic fluid dynamics, Gravitational collapse, Numerical methods, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/9604029},
pages = {3--19},
publisher = {University of Houston},
series = {Houston Journal of Mathematics},
title = {Spectral methods in general relativity -- toward the simulation of 3D-gravitational collapse of neutron stars},
year = {1996}
}
@article{Bonazzola-etal-1998:spectral-methods-in-gr-astrophysics,
adsurl = {http://adsabs.harvard.edu/abs/1999JCoAM.109..433B},
author = {Bonazzola, S. and Gourgoulhon, E. and Marck, J.-A.},
cited = {9 January 2006},
doi = {10.1016/S0377-0427(99)00167-3},
journal = {J. Comput. Appl. Math.},
keywords = {Boundary conditions, Boundary value problems, Initial boundary value problem, Numerical methods, Numerical relativity, Relativistic fluids, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/9811089},
pages = {433--473},
title = {Spectral methods in general astrophysics},
volume = {109},
year = {1999}
}
@article{Booth-review,
author = {Booth, I.},
cited = {9 January 2006},
doi = {10.1139/p05-063},
journal = {Can. J. Phys.},
keywords = {Apparent horizons, Area increase law, Black holes, Boundary conditions, Causal structure, Dynamical horizons, Event horizons, Generic collapse, Horizons, Isolated horizons, Killing horizons, Null surfaces, Quasi-local black holes, Three-manifolds, Trapped surfaces, Trapping horizons},
onlineversion = {http://arXiv.org/abs/gr-qc/0508107},
pages = {1073--1099},
title = {Black hole boundaries},
volume = {83},
year = {2005}
}
@book{Boyd00,
address = {Mineola, NY},
author = {Boyd, J. P.},
edition = {2nd rev.},
gbs_id = {lEWnQWyzLQYC},
keywords = {Boundary conditions, Boundary value problems, Initial boundary value problem, Numerical methods, Spectral methods},
publisher = {Dover Publications},
title = {Chebyshev and Fourier Spectral Methods},
year = {2001}
}
@online{Brankin-Gladwell-Shampine-1992,
author = {Brankin, R. W. and Gladwell, I. and Shampine, L. F.},
cited = {9 January 2006},
format = {other},
keywords = {Finite difference methods, Numerical methods, Ordinary differential equations},
publisher = {Dept. of Mathematics, Southern Methodist University, Dallas, TX},
title = {RKSUITE: A Suite of Runge--Kutta Codes for the Initial Value Problem for ODEs},
url = {http://www.netlib.org/ode/rksuite/},
year = {1992}
}
@book{Brent2002,
address = {Mineola, U.S.A.},
author = {Brent, R. P.},
gbs_id = {6Ay2biHG-GEC},
keywords = {Minimization, Numerical methods},
note = {Reprint of 1973 original edition},
publisher = {Dover Publications},
title = {Algorithms for Minimization Without Derivatives},
year = {2002}
}
@article{Brewin-2000:convergence-of-Regge-calculus,
author = {Brewin, L. C.},
cited = {9 January 2006},
doi = {10.1023/A:1001937108480},
journal = {Gen. Relativ. Gravit.},
keywords = {Approximation methods, Numerical relativity, Regge calculus},
onlineversion = {http://arXiv.org/abs/gr-qc/9502043},
pages = {897--918},
title = {Is the Regge Calculus a Consistent Approximation to General Relativity?},
volume = {32},
year = {2000}
}
@article{Brewin-Gentle-2001:convergence-of-Regge-calculus,
author = {Brewin, L. C. and Gentle, A. P.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/18/3/311},
journal = {Class. Quantum Grav.},
keywords = {Approximation methods, Numerical relativity, Regge calculus},
onlineversion = {http://arXiv.org/abs/gr-qc/0006017},
pages = {517--525},
title = {On the Convergence of Regge Calculus to General Relativity},
volume = {18},
year = {2001}
}
@book{Briggs-Henson-McCormick-2000:multigrid,
address = {Philadelphia, U.S.A.},
author = {Briggs, W. L. and Henson, V. E. and McCormick, S. F.},
edition = {2nd},
gbs_id = {SRAZwqAkrQMC},
keywords = {Boundary conditions, Boundary value problems, Initial boundary value problem, Numerical methods, Spectral methods},
publisher = {SIAM},
title = {A Multigrid Tutorial},
year = {2000}
}
@article{Brill63,
adsurl = {http://adsabs.harvard.edu/abs/1963PhRv..131..471B},
author = {Brill, D. R. and Lindquist, R. W.},
doi = {10.1103/PhysRev.131.471},
journal = {Phys. Rev.},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Boundary value problems, Horizons, Maximal hypersurfaces, Multi black hole solutions, Numerical relativity, Spectral methods},
pages = {471--476},
title = {Interaction Energy in Geometrostatics},
volume = {131},
year = {1963}
}
@article{Cadez74,
author = {{\v{C}}ade{\v{z}}, A.},
journal = {Ann. Phys. (N.Y.)},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Boundary value problems, Horizons, Maximal hypersurfaces, Multi black hole solutions, Numerical relativity, Ordinary differential equations},
pages = {449--457},
title = {Apparent Horizons in the Two-Black-Hole Problem},
volume = {83},
year = {1974}
}
@online{carpet-author-and-web-site,
author = {Schnetter, E.},
cited = {9 January 2006},
format = {project homepage},
keywords = {Numerical methods, Partial differential equations},
publisher = {Center for Computation and Technology, Louisiana State University},
title = {CarpetCode: A mesh refinement driver for Cactus},
url = {http://www.carpetcode.org}
}
@phdthesis{Caveny-2002,
address = {Austin, U.S.A.},
author = {Caveny, S. A.},
format = {phd},
keywords = {Apparent horizons, Black hole collisions, Black holes, Distorted black holes, Event horizons, Finite difference methods, Multi black hole spacetimes, Numerical methods, Numerical relativity, Topology change},
school = {University of Texas at Austin},
title = {Tracking Black Holes in Numerical Relativity: Foundations and Applications},
year = {2002}
}
@article{Caveny-Anderson-Matzner-2003a,
author = {Caveny, S. A. and Anderson, M. and Matzner, R. A.},
cited = {9 January 2006},
journal = {Phys. Rev. D},
keywords = {Black hole collisions, Black holes, Distorted black holes, Event horizons, Finite difference methods, Multi black hole spacetimes, Numerical methods, Numerical relativity, Topology change},
onlineversion = {http://arXiv.org/abs/gr-qc/0303099},
pages = {104009},
title = {Tracking Black Holes in Numerical Relativity},
volume = {68},
year = {2003}
}
@article{Caveny-Matzner-2003a,
author = {Caveny, S. A. and Matzner, R. A.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.68.104003},
eid = {104003},
eprint = {gr-qc/0303109},
journal = {Phys. Rev. D},
keywords = {Black hole collisions, Black holes, Critical phenomena, Distorted black holes, Event horizons, Finite difference methods, Multi black hole spacetimes, Numerical methods, Numerical relativity, Topology change},
onlineversion = {http://arXiv.org/abs/gr-qc/0303109},
pages = {1--13},
title = {Adaptive event horizon tracking and critical phenomena in binary black hole coalescence},
volume = {68},
year = {2003}
}
@phdthesis{Choptuik86,
address = {Vancouver, Canada},
author = {Choptuik, M. W.},
format = {phd},
keywords = {Apparent horizons, Boundary conditions, Finite difference methods, Initial boundary value problem, Mass functions, Numerical methods, Numerical relativity, Partial differential equations, Scalar fields, Spherical symmetry},
school = {University of British Columbia},
title = {A Study of Numerical Techniques for Radiative Problems in General Relativity},
year = {1986}
}
@inproceedings{Choptuik89,
address = {Cambridge, U.K.; New York, U.S.A.},
author = {Choptuik, M. W.},
booktitle = {Frontiers in Numerical Relativity},
conference = {Proceedings of the International Workshop on Numerical Relativity, University of Illinois at Urbana-Champaign (Urbana-Champaign, Illinois, USA), May 9\,--\,13, 1988},
editor = {Evans, C. R. and Finn, L. S. and Hobill, D. W.},
keywords = {Apparent horizons, Boundary conditions, Finite difference methods, Initial boundary value problem, Mass functions, Numerical methods, Numerical relativity, Partial differential equations, Scalar fields, Spherical symmetry},
pages = {206--221},
publisher = {Cambridge University Press},
title = {Experiences with an Adaptive Mesh Refinement Algorithm in Numerical Relativity},
year = {1989}
}
@article{Chrusciel-Galloway-1998:non-differentiable-horizons,
author = {Chru{\'{s}}ciel, P. T. and Galloway, G. J.},
cited = {9 January 2006},
journal = {Commun. Math. Phys.},
keywords = {Event horizons, Horizon geometry},
onlineversion = {http://arXiv.org/abs/gr-qc/9611032},
pages = {449--470},
title = {Horizons Non-Differentiable on a Dense Set},
volume = {193},
year = {1998}
}
@phdthesis{Cook90,
address = {Chapel Hill, U.S.A.},
author = {Cook, G. B.},
format = {phd},
keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Black holes, Boundary value problems, Constraint equations, Distorted black holes, Elliptic equations, Finite difference methods, Multi black hole solutions, Numerical methods, Numerical relativity, Rotating black holes},
school = {University of North Carolina at Chapel Hill},
title = {Initial Data for the Two-Body Problem of General Relativity},
year = {1990}
}
@article{Cook90a,
author = {Cook, G. B. and York Jr, J. W.},
journal = {Phys. Rev. D},
keywords = {Angular momentum, Axisymmetric black holes, Black holes, Boundary value problems, Constraint equations, Distorted black holes, Elliptic equations, Finite difference methods, Maximal hypersurfaces, Numerical methods, Numerical relativity},
pages = {1077--1085},
title = {Apparent Horizons for Boosted or Spinning Black Holes},
volume = {41},
year = {1990}
}
@article{Cook92,
author = {Cook, G. B. and Abrahams, A. M.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Boundary value problems, Causal structure, Elliptic equations, Event horizons, Finite difference methods, Horizon geometry, Maximal hypersurfaces, Numerical methods, Numerical relativity, Trapped surfaces},
pages = {702--713},
title = {Horizon Structure of Initial-Data Sets for Axisymmetric Two-Black-Hole Collisions},
volume = {46},
year = {1992}
}
@article{Curtis-Reid-1974,
author = {Curtis, A. R. and Reid, J. K.},
journal = {J. Inst. Math. Appl.},
keywords = {Numerical methods},
pages = {121--126},
title = {The Choice of Step Lengths When Using Differences to Approximate Jacobian Matrices},
volume = {13},
year = {1974}
}
@article{Davis-2002a-UMFPACK-report,
author = {Davis, T. A.},
cited = {9 January 2006},
doi = {10.1145/992200.992205},
journal = {ACM Trans. Math. Software},
keywords = {Linear equations, Numerical methods},
note = {TR-02-001},
onlineversion = {http://www.cise.ufl.edu/~davis/},
pages = {165--195},
title = {A column pre-ordering strategy for the unsymmetric-pattern multifrontal method},
volume = {30},
year = {2004}
}
@article{Davis-2002b-UMFPACK-report,
author = {Davis, T. A.},
cited = {9 January 2006},
doi = {10.1145/992200.992206},
journal = {ACM Trans. Math. Software},
keywords = {Linear equations, Numerical methods},
note = {TR-02-002},
onlineversion = {http://www.cise.ufl.edu/~davis/},
pages = {196--199},
title = {Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method},
volume = {30},
year = {2004}
}
@article{Davis-Duff-1997-UMFPACK,
author = {Davis, T. A. and Duff, I. S.},
doi = {10.1137/S0895479894246905},
journal = {SIAM J. Matrix Anal. Appl.},
keywords = {Linear equations, Numerical methods},
pages = {140--158},
title = {An unsymmetric-pattern multifrontal method for sparse LU factorization},
volume = {18},
year = {1997}
}
@article{Davis-Duff-1999-UMFPACK,
author = {Davis, T. A. and Duff, I. S.},
doi = {10.1145/305658.287640},
journal = {ACM Trans. Math. Software},
keywords = {Linear equations, Numerical methods},
pages = {1--19},
title = {A combined unifrontal/multifrontal method for unsymmetric sparse matrices},
volume = {25},
year = {1999}
}
@book{Dennis-Schnabel-1996,
address = {Philadelphia, U.S.A.},
author = {Dennis Jr, J. E. and Schnabel, R. B.},
keywords = {Minimization, Numerical methods, Nonlinear algebraic equations},
publisher = {SIAM},
title = {Numerical Methods for Unconstrained Optimization and Nonlinear Equations},
year = {1996}
}
@article{Diener03a,
author = {Diener, P.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/20/22/014},
journal = {Class. Quantum Grav.},
keywords = {Black holes, Event horizons, Kerr black holes, Multi black hole spacetimes, Null surfaces, Numerical methods, Numerical relativity, Topology change},
onlineversion = {http://arXiv.org/abs/gr-qc/0305039},
pages = {4901--4917},
title = {A New General Purpose Event Horizon Finder for 3D},
volume = {20},
year = {2003}
}
@article{Diener-etal-2006a,
author = {Diener, P. and Herrmann, F. and Pollney, D. and Schnetter, E. and Seidel, E. and Takahashi, R. and Thornburg, J. and Ventrella, J.},
cited = {3 October 2006},
doi = {10.1103/PhysRevLett.96.121101},
journal = {Phys. Rev. Lett.},
keywords = {Apparent horizons, Black hole collisions, Multi black hole spacetimes, Numerical relativity},
onlineversion = {http://arXiv.org/abs/gr-qc/0512108},
pages = {121101},
title = {Accurate Evolution of Orbiting Binary Black Holes},
volume = {96},
year = {2006}
}
@misc{Diener-2007-modifying-EHFinder-to-work-with-Carpet,
author = {Diener, P.},
format = {personal communication},
keywords = {Event horizons, Finite difference methods, Numerical methods},
year = {2007}
}
@article{Dreyer02a,
author = {Dreyer, O. and Krishnan, B. and Shoemaker, D. and Schnetter, E.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.67.024018},
eid = {024018},
journal = {Phys. Rev. D},
keywords = {Angular momentum, Apparent horizons, Black holes, Isolated horizons, Kerr black holes, Killing field, Numerical methods, Numerical relativity, Quasi-local angular momentum, Quasi-local black holes, Quasi-local mass, Rotating black holes, Three-manifolds},
numpages = {14},
onlineversion = {http://arXiv.org/abs/gr-qc/0206008},
title = {Introduction to isolated horizon in numerical relativity},
volume = {67},
year = {2003}
}
@book{Duff-Erisman-Reid-1986,
address = {Oxford, U.K.; New York, U.S.A.},
author = {Duff, I. S. and Erisman, A. M. and Reid, J. K.},
keywords = {Linear equations, Numerical methods},
publisher = {Oxford University Press},
title = {Direct Methods for Sparse Matrices},
year = {1986}
}
@article{DuFort-Frankel-1953,
author = {Du Fort, E. C. and Frankel, S. P.},
journal = {Math. Tables Aids Comput.},
keywords = {Finite difference methods, Numerical methods, Parabolic equations},
pages = {135--152},
title = {Stability Conditions in the Numerical Treatment of Parabolic Differential Equations},
volume = {7},
year = {1953}
}
@phdthesis{Dykema80,
address = {Austin, U.S.A.},
author = {Dykema, P. G.},
format = {phd},
keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Black hole formation, Black holes, Brill waves, Computational fluid dynamics, Distorted black holes, Finite difference methods, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Ordinary differential equations, Partial differential equations, Relativistic fluid dynamics},
school = {University of Texas at Austin},
title = {The Numerical Simulation of Axially Symmetric Gravitational Collapse},
year = {1980}
}
@article{Eardley75,
author = {Eardley, D. M.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black hole formation, Black holes, Collisionless matter, Dust, Elliptic equations, Finite difference methods, Gravitational collapse, Prolate collapse},
pages = {3072--3076},
title = {Gravitational Collapse of Marginally Bound Spheroids: Initial Conditions},
volume = {12},
year = {1975}
}
@phdthesis{Eppley75,
address = {Princeton, U.S.A.},
author = {Eppley, K. R.},
format = {phd},
keywords = {ADM formalism, Apparent horizons, Asymptotically flat data, Axisymmetric black holes, Black hole collisions, Black holes, Boundary value problems, Elliptic equations, Finite difference methods, Foliations, Instability, Maximal hypersurfaces, Maximal slicing, Multi black hole spacetimes, Numerical methods, Numerical relativity, Ordinary differential equations, Partial differential equations},
school = {Princeton University},
title = {The numerical evolution of the collision of two black holes},
year = {1975}
}
@article{Eppley77,
author = {Eppley, K. R.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Brill waves, Finite difference methods, Mass formula, Maximal slicing, Numerical methods, Numerical relativity, Partial differential equations, Quasi-local mass, Scalar curvature},
pages = {1609--1614},
title = {Evolution of time-symmetric gravitational waves: Initial data and apparent horizons},
volume = {16},
year = {1977}
}
@book{Fornberg-1998-pseudospectral-intro,
address = {Cambridge; New York},
author = {Fornberg, B.},
gbs_id = {IqJoihDba3gC},
keywords = {Boundary conditions, Boundary value problems, Initial boundary value problem, Numerical methods, Spectral methods},
publisher = {Cambridge University Press},
series = {Cambridge Monographs on Mathematical Physics},
title = {A Practical Guide to Pseudospectral Methods},
year = {1998}
}
@book{FMM77,
address = {Englewood Cliffs, U.S.A.},
author = {Forsythe, G. E. and Malcolm, M. A. and Moler, C. B.},
cited = {9 January 2006},
keywords = {Finite difference methods, Numerical methods, Ordinary differential equations},
onlineversion = {http://www.netlib.org/fmm/},
publisher = {Prentice-Hall},
title = {Computer Methods for Mathematical Computations},
year = {1977}
}
@article{Gentle-Miller-1998:Regge-calculus-model-of-Kasner,
adsurl = {http://adsabs.harvard.edu/abs/1998CQGra..15..389G},
author = {Gentle, A. P. and Miller, W. A.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/15/2/013},
journal = {Class. Quantum Grav.},
keywords = {Cosmological models, Generic collapse, Numerical methods, Numerical relativity, Regge calculus},
onlineversion = {http://arXiv.org/abs/gr-qc/9706034},
pages = {389--405},
title = {A fully (3+1)-dimensional Regge calculus model of the Kasner cosmology},
volume = {15},
year = {1965}
}
@article{Gentle-2002:Regge-calculus-review,
author = {Gentle, A. P.},
cited = {9 January 2006},
doi = {10.1023/A:1020128425143},
journal = {Gen. Relativ. Gravit.},
keywords = {Black holes, Brill waves, Distorted black holes, Numerical methods, Numerical relativity, Regge calculus, Schwarzschild solution},
onlineversion = {http://arXiv.org/abs/gr-qc/0408006},
pages = {1701--1718},
title = {Regge Calculus: A Unique Tool for Numerical Relativity},
volume = {34},
year = {2002}
}
@article{Grayson-1987,
author = {Grayson, M. A.},
journal = {J. Differ. Geom.},
keywords = {Inverse mean curvature flow, Parabolic equations, Ricci flow},
pages = {285--314},
title = {The Heat Equation Shrinks Embedded Plane Curves to Round Points},
volume = {26},
year = {1987}
}
@inproceedings{Goodale02a,
address = {Berlin, Germany; New York, U.S.A.},
author = {Goodale, T. and Allen, G. and Lanfermann, G. and Mass{\'{o}}, J. and Radke, T. and Seidel, E. and Shalf, J.},
booktitle = {High Performance Computing for Computational Science (VECPAR 2002)},
conference = {5th International Conference, Porto, Portugal, June 26\,--\,28, 2002: Selected papers and invited talks},
editor = {Palma, J. M. L. M.and Dongarra, J. and Hern{\'{a}}ndez, V. and Sousa, A. A.},
keywords = {Numerical methods},
pages = {197--227},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
title = {The Cactus Framework and Toolkit: Design and Applications},
volume = {2565},
year = {2003}
}
@book{Gottlieb-Orszag:pseudospectral,
address = {Philadelphia},
author = {Gottlieb, D. and Orszag, S. A.},
gbs_id = {ycITkwWMRVkC},
keywords = {Boundary conditions, Boundary value problems, Initial boundary value problem, Numerical methods, Spectral methods},
note = {Based on a series of lectures presented at the NSF-CBMS regional conference held at Old Dominion University from August 2\,--\,6, 1976},
publisher = {SIAM},
series = {Regional Conference Series in Applied Mathematics},
title = {Numerical Analysis of Spectral Methods: Theory and Applications},
volume = {26},
year = {1977}
}
@article{Grandclement-etal-2000:multi-domain-spectral-method,
adsurl = {http://adsabs.harvard.edu/abs/2001JCoPh.170..231G},
author = {Grandcl{\'{e}}ment, P. and Bonazzola, S. and Gourgoulhon, E. and Marck, J.-A.},
cited = {9 January 2006},
doi = {10.1006/jcph.2001.6734},
journal = {J. Comput. Phys.},
keywords = {Black holes, Boundary value problems, Constraint equations, Helical Killing vectors, Numerical methods, Numerical relativity, Rotating black holes, Spectral methods, Innermost stable circular orbits (ISCO)},
onlineversion = {http://arXiv.org/abs/gr-qc/0003072},
pages = {231--260},
title = {A multidomain spectral method for scalar and vectorial poisson equations with noncompact sources},
volume = {170},
year = {2001}
}
@article{Grandclement02,
adsurl = {http://adsabs.harvard.edu/abs/2002PhRvD..65d4021G},
author = {Grandcl{\'{e}}ment, P. and Gourgoulhon, E. and Bonazzola, S.},
doi = {10.1103/PhysRevD.65.044021},
eid = {044021},
journal = {Phys. Rev. D},
keywords = {Black holes, Boundary value problems, Constraint equations, Helical Killing vectors, Numerical methods, Numerical relativity, Rotating black holes, Spectral methods, Innermost stable circular orbits (ISCO)},
numpages = {18},
title = {Binary black holes in circular orbits. II. Numerical methods and first results},
volume = {65},
year = {2002}
}
@article{Gundlach97a,
author = {Gundlach, C.},
cited = {9 January 2006},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Inverse mean curvature flow, Multi black hole solutions, Numerical methods, Numerical relativity, Parabolic equations, Ricci flow, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/9707050},
pages = {863--875},
title = {Pseudo-spectral apparent horizon finders: An efficient new algorithm},
volume = {57},
year = {1998}
}
@inproceedings{Hawking73,
address = {New York},
author = {Hawking, S. W.},
booktitle = {Black Holes},
conference = {Based on lectures given at the 23rd session of the Summer School of Les Houches, 1972},
editor = {DeWitt, C. M. and DeWitt, B. S.},
keywords = {Black holes, Event horizons},
pages = {1--56},
publisher = {Gordon and Breach},
title = {The Event Horizon},
year = {1973}
}
@book{Hawking73a,
address = {Cambridge},
author = {Hawking, S. W. and Ellis, G. F. R.},
gbs_id = {QagG{\_}KI7Ll8C},
keywords = {Apparent horizons, Black holes, Event horizons, Singularity theorems, Topology change, Trapped surfaces},
publisher = {Cambridge University Press},
series = {Cambridge Monographs on Mathematical Physics},
title = {The Large Scale Structure of Space-Time},
year = {1973}
}
@article{Hayward94a,
author = {Hayward, S. A.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.49.6467},
eprint = {gr-qc/9303006},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black holes, Event horizons, Topology change, Trapped surfaces, Trapping horizons},
onlineversion = {http://arXiv.org/abs/gr-qc/9306006},
pages = {6467--6474},
title = {General laws of black-hole dynamics},
volume = {49},
year = {1994}
}
@inproceedings{Hindmarsh-1983,
address = {Amsterdam, Netherlands; New York, U.S.A.},
author = {Hindmarsh, A. C.},
booktitle = {Scientific Computing: Applications of Mathematics and Computing to the Physical Sciences},
cited = {9 January 2006},
conference = {Based on papers presented at the Tenth IMACS World Congress on System Simulation and Scientific Computation, held in Montreal, Canada, August 8\,--\,13, 1982},
editor = {Stepleman, R. S. et al.},
keywords = {Finite difference methods, Numerical methods, Ordinary differential equations},
onlineversion = {http://www.netlib.org/odepack/index.html},
pages = {55--64},
publisher = {North-Holland},
series = {IMACS Transactions on Scientific Computing},
title = {ODEPACK, A Systematized Collection of ODE Solvers},
volume = {1},
year = {1983}
}
@article{Hochbruck-etal-1998:exponential-integrator,
author = {Hochbruck, M. and Lubich, C. and Selhofer, H.},
doi = {10.1137/S1064827595295337},
journal = {SIAM J. Sci. Comput.},
keywords = {Finite difference methods, Numerical methods, Ordinary differential equations},
pages = {1552--1574},
title = {Exponential Integrators for Large Systems of Differential Equations},
volume = {19},
year = {1998}
}
@article{Hornung-Kohn-2002:SAMRAI--managing-complexity,
author = {Hornung, R. D. and Kohn, S. R.},
doi = {10.1002/cpe.652},
journal = {Concurr. Comput. Pract. Exp.},
keywords = {Numerical methods, Partial differential equations},
pages = {347--368},
title = {Managing application complexity in the SAMRAI object-oriented framework},
volume = {14},
year = {2002}
}
@article{Hornung-etal-2006:SAMRAI--managing-complex-data-geometry,
author = {Hornung, R. D. and Wissink, A. M. and Kohn, S. R.},
doi = {10.1007/s00366-006-0038-6},
journal = {Eng. Comput.},
keywords = {Numerical methods, Partial differential equations},
pages = {181--195},
title = {Managing complex data and geometry in parallel structured AMR applications},
volume = {22},
year = {2006}
}
@article{Hughes94a,
author = {Hughes, S. A. and Keeton II, C. R. and Walker, P. and Walsh, K. T. and Shapiro, S. L. and Teukolsky, S. A.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black holes, Event horizons, Geodesics, Kerr black holes, Numerical methods, Numerical relativity, Ordinary differential equations, Schwarzschild solution, Topology change},
pages = {4004--4015},
title = {Finding Black Holes in Numerical Spacetimes},
volume = {49},
year = {1994}
}
@phdthesis{Huq96,
address = {Austin, U.S.A.},
author = {Huq, M. F.},
format = {phd},
keywords = {Apparent horizons, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity},
school = {The University of Texas at Austin},
title = {Apparent Horizon Location in Numerical Spacetimes},
year = {1996}
}
@article{Huq00,
author = {Huq, M. F. and Choptuik, M. W. and Matzner, R. A.},
cited = {9 January 2006},
eid = {084024},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity},
onlineversion = {http://arXiv.org/abs/gr-qc/0002076},
title = {Locating Boosted Kerr and Schwarzschild Apparent Horizons},
volume = {66},
year = {2002}
}
@article{Husa99a,
adsurl = {http://adsabs.harvard.edu/abs/1999PhRvD..60h4019H},
archiveprefix = {arXiv},
author = {Husa, S. and Winicour, J.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.60.084019},
eid = {084019},
eprint = {gr-qc/9905039},
journal = {Phys. Rev. D},
keywords = {Black hole collisions, Event horizons, Multi black hole spacetimes, Numerical relativity, Topology change},
numpages = {13},
onlineversion = {http://arXiv.org/abs/gr-qc/9905039},
title = {Asymmetric merger of black holes},
volume = {60},
year = {1999}
}
@article{Gourgoulhon-Jaramillo-Review,
adsurl = {http://adsabs.harvard.edu/abs/2006PhR...423..159G},
author = {Gourgoulhon, E. and Jaramillo, J. L.},
cited = {9 January 2006},
doi = {10.1016/j.physrep.2005.10.005},
journal = {Phys. Rep.},
keywords = {ADM formalism, Apparent horizons, Black holes, Dynamical horizons, Isolated horizons, Null surfaces, Three-manifolds},
onlineversion = {http://arXiv.org/abs/gr-qc/0503113},
pages = {159--294},
title = {A 3+1 perspective on null hypersurfaces and isolated horizons},
volume = {423},
year = {2006}
}
@book{Kahaner-Moler-Nash-1989,
address = {Englewood Cliffs, U.S.A.},
author = {Kahaner, D. and Moler, C. B. and Nash, S.},
keywords = {Finite difference methods, Numerical methods, Ordinary differential equations},
note = {Revised and (greatly) expanded edition of Forsythe, G.E. and Malcolm, M.A. and Moler, C.B, ``Computer methods for mathematical computations''(1977)},
publisher = {Prentice Hall},
title = {Numerical Methods and Software},
year = {1989}
}
@article{Kemball91a,
author = {Kemball, A. J. and Bishop, N. T.},
doi = {10.1088/0264-9381/8/7/012},
journal = {Class. Quantum Grav.},
keywords = {Apparent horizons, Multi black hole solutions, Numerical methods, Numerical relativity, Spectral methods},
pages = {1361--1367},
title = {The numerical determination of apparent horizons},
volume = {8},
year = {1991}
}
@article{Kershaw1978:ilucg,
author = {Kershaw, D. S.},
doi = {10.1016/0021-9991(78)90098-0},
journal = {J. Comput. Phys.},
keywords = {Linear equations, Numerical methods},
pages = {43--65},
title = {The Incomplete Cholesky-Conjugate Gradient Method for Interative Solution of Linear Equations},
volume = {26},
year = {1978}
}
@article{Kidder99a,
adsurl = {http://adsabs.harvard.edu/abs/2000PhRvD..62h4026K},
author = {Kidder, L. E. and Finn, L. S.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.62.084026},
eid = {084026},
journal = {Phys. Rev. D},
keywords = {Axial symmetry, Boundary value problems, Brill waves, Constraint equations, Numerical methods, Numerical relativity, Rotating black holes, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/9911014},
pages = {1--13},
title = {Spectral methods for numerical relativity: The initial data problem},
volume = {62},
year = {2000}
}
@article{Kidder00a,
adsurl = {http://adsabs.harvard.edu/abs/2000PhRvD..62h4032K},
archiveprefix = {arXiv},
author = {Kidder, L. E. and Scheel, M. A. and Teukolsky, S. A. and Carlson, E. D. and Cook, G. B.},
cited = {9 January 2006},
doi = {10.1103/PhysRevD.62.084032},
eid = {084032},
eprint = {gr-qc/0005056},
journal = {Phys. Rev. D},
keywords = {Black holes, Boundary conditions, Hyperbolic partial differential equations, Initial boundary value problem, Numerical methods, Numerical relativity, Spectral methods, Spherical symmetry},
onlineversion = {http://arXiv.org/abs/gr-qc/0005056},
primaryclass = {gr-qc},
title = {Black hole evolution by spectral methods},
volume = {62},
year = {2000}
}
@unpublished{Kidder00b,
author = {Kidder, L. E. and Scheel, M. A. and Teukolsky, S. A. and Cook, G. B.},
conference = {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},
format = {conference paper},
keywords = {Black holes, Boundary conditions, Hyperbolic partial differential equations, Initial boundary value problem, Numerical methods, Numerical relativity, Spectral methods},
title = {Spectral Evolution of Einstein's Equations},
year = {2000}
}
@article{Kriele97,
author = {Kriele, M. and Hayward, S. A.},
doi = {10.1063/1.532010},
journal = {J. Math. Phys.},
keywords = {Apparent horizons, Black holes, Trapped surfaces},
pages = {1593--1604},
title = {Outer trapped surfaces and their apparent horizon},
volume = {38},
year = {1997}
}
@article{Lehner-etal-1999:BH-coalescence-geometry,
adsurl = {http://adsabs.harvard.edu/abs/1999PhRvD..60d4005L},
archiveprefix = {arXiv},
author = {Lehner, L. and Bishop, N. T. and G{\'{o}}mez, R. and Szil{\'{a}}gyi, B. and Winicour, J.},
doi = {10.1103/PhysRevD.60.044005},
eid = {044005},
eprint = {gr-qc/9809034},
journal = {Phys. Rev. D},
keywords = {Black hole collisions, Event horizons, Multi black hole spacetimes, Numerical relativity, Topology change},
numpages = {10},
title = {Exact solutions for the intrinsic geometry of black hole coalescence},
volume = {60},
year = {1999}
}
@online{Lehner-etal-BH-bagels-movies,
author = {Lehner, L. and G{\'{o}}mez, R. and Husa, S. and Szil{\'{a}}gyi, B. and Bishop, N. T. and Winicour, J.},
cited = {9 January 2006},
format = {institutional homepage},
keywords = {Black hole collisions, Event horizons, Multi black hole spacetimes, Numerical relativity, Topology change},
publisher = {Pittsburgh Supercomputing Center},
title = {Bagels Form When Black Holes Collide},
url = {http://www.psc.edu/research/graphics/gallery/winicour.html}
}
@article{Leiler_Rezzolla06,
author = {Leiler, G. and Rezzolla, L.},
cited = {3 October 2006},
eid = {044001},
journal = {Phys. Rev. D},
keywords = {Finite difference methods, Numerical methods, Partial differential equations},
onlineversion = {http://arXiv.org/abs/gr-qc/0601139},
title = {On the iterated Crank--Nicolson method for hyperbolic and parabolic equations in numerical relativity},
volume = {73},
year = {2006}
}
@article{Libson94a,
author = {Libson, J. and Mass{\'{o}}, J. and Seidel, E. and Suen, W.-M. and Walker, P.},
eprint = {gr-qc/9412068},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black holes, Distorted black holes, Event horizons, Kerr black holes, Multi black hole spacetimes, Null surfaces, Numerical methods, Numerical relativity, Rotating black holes, Schwarzschild solution},
pages = {4335--4350},
title = {Event horizons in numerical relativity: Methods and tests},
volume = {53},
year = {1996}
}
@inproceedings{Libson95a,
address = {Singapore; River Edge, U.S.A.},
author = {Libson, J. and Mass{\'{o}}, J. and Seidel, E. and Suen, W.-M.},
booktitle = {The Seventh Marcel Grossmann Meeting: On recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories},
conference = {Proceedings of the meeting held at Stanford University, July 24\,--\,30, 1994},
editor = {Jantzen, R. T. and Keiser, G. M.},
keywords = {Apparent horizons, Numerical methods, Numerical relativity, Spectral methods},
pages = {631},
publisher = {World Scientific},
title = {A 3D Apparent Horizon Finder},
year = {1996}
}
@misc{Lin-Novak-2006:LORENE-AHfinder,
author = {Lin, L.-M. and Novak, J.},
format = {personal communication},
keywords = {Apparent horizons, Kerr black holes, Numerical methods, Numerical relativity, Spectral methods},
note = {Personal communication from Lap-Ming Lin to Jonathan Thornburg},
title = {Three-dimensional apparent horizon finder in LORENE},
year = {2006}
}
@article{Lorensen-Cline-1987:marching-cubes,
author = {Lorensen, W. E. and Cline, H. E.},
doi = {10.1145/37402.37422},
journal = {SIGGRAPH Comput. Graph.},
keywords = {Numerical methods},
pages = {163--169},
title = {Marching cubes: A high resolution 3D surface construction algorithm},
volume = {21},
year = {1987}
}
@misc{Madderom-1984:ILUCG,
author = {Madderom, P.},
format = {unknown},
keywords = {Linear equations, Numerical methods},
note = {Fortran 66 subroutine},
title = {Incomplete LU-Decomposition -- Conjugate Gradient},
year = {1984}
}
@article{MacNeice00,
author = {MacNeice, P. and Olson, K. M. and Mobarry, C. and de Fainchtein, R. and Packer, C.},
doi = {10.1016/S0010-4655(99)00501-9},
journal = {Comput. Phys. Commun.},
keywords = {Numerical methods},
pages = {330--354},
title = {PARAMESH: A parallel adaptive mesh refinement community toolkit},
volume = {126},
year = {2000}
}
@article{Matzner95a,
adsurl = {http://adsabs.harvard.edu/abs/1995Sci...270..941M},
author = {Matzner, R. A. and Seidel, E. and Shapiro, S. L. and Smarr, L. L. and Suen, W.-M. and Teukolsky, S. A. and Winicour, J.},
doi = {10.1126/science.270.5238.941},
journal = {Science},
keywords = {Axial symmetry, Axisymmetric black holes, Black hole collisions, Black holes, Causal structure, Collisionless matter, Dust, Event horizons, Finite difference methods, Geodesics, Gravitational collapse, Multi black hole spacetimes, Numerical relativity, Partial differential equations},
pages = {941--947},
title = {Geometry of a Black Hole Collision},
volume = {270},
year = {1995}
}
@article{Metzger04,
author = {Metzger, J.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/21/19/010},
journal = {Class. Quantum Grav.},
keywords = {Apparent horizons, Inverse mean curvature flow, Ricci flow, Numerical methods, Numerical relativity, Trapped surfaces},
onlineversion = {http://arXiv.org/abs/gr-qc/0408059},
pages = {4625--4646},
title = {Numerical computation of constant mean curvature surfaces using finite elements},
volume = {21},
year = {2004}
}
@article{Miller-1995:4th-order-Regge-calculus,
author = {Miller, M. A.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/12/12/019},
journal = {Class. Quantum Grav.},
keywords = {Approximation methods, Numerical relativity, Regge calculus},
onlineversion = {http://arXiv.org/abs/gr-qc/9502044},
pages = {3037--3051},
title = {Regge Calculus as a Fourth Order Method in Numerical Relativity},
volume = {12},
year = {1995}
}
@article{Misner-Sharp-1964,
author = {Misner, C. W. and Sharp, D. H.},
doi = {10.1103/PhysRev.136.B571},
journal = {Phys. Rev.},
keywords = {Mass functions, Relativistic fluids, Spherical symmetry},
pages = {B571--B576},
title = {Relativistic equations for adiabatic, spherically symmetric gravitational collapse},
volume = {136},
year = {1964}
}
@book{Misner73,
address = {San Francisco},
adsurl = {http://adsabs.harvard.edu/abs/1973grav.book.....M},
author = {Misner, C. W. and Thorne, K. S. and Wheeler, J. A.},
keywords = {ADM formalism, Mass functions},
publisher = {W. H. Freeman},
title = {Gravitation},
year = {1973}
}
@article{Nakamura84,
adsurl = {http://adsabs.harvard.edu/abs/1984PhLA..106..235N},
author = {Nakamura, T. and Kojima, Y. and Oohara, K.},
doi = {10.1016/0375-9601(84)91016-8},
journal = {Phys. Lett. A},
keywords = {Apparent horizons, Multi black hole solutions, Numerical methods, Numerical relativity, Spectral methods},
pages = {235--238},
title = {A method of determining apparent horizons in three-dimensional numerical relativity},
volume = {106},
year = {1984}
}
@article{Oohara85,
author = {Oohara, K. and Nakamura, T. and Kojima, Y.},
doi = {10.1016/0375-9601(85)90423-2},
journal = {Phys. Lett. A},
keywords = {Apparent horizons, Multi black hole solutions, Numerical methods, Spectral methods},
pages = {452--455},
title = {Apparent Horizons of Time-Symmetric Initial Value for Three Black Holes},
volume = {107},
year = {1985}
}
@inproceedings{Oohara86,
address = {Singapore; Philadelphia, U.S.A.},
author = {Oohara, K.},
booktitle = {Gravitational Collapse and Relativity},
conference = {Proceedings of Yamada Conference XIV, Kyoto International Conference Hall, Japan, April 7\,--\,11, 1986},
editor = {Sato, H. and Nakamura, T.},
keywords = {Apparent horizons, Black hole collisions, Multi black hole solutions, Numerical methods, Spectral methods},
pages = {313--319},
publisher = {World Scientific},
title = {Apparent Horizon of Initial Data for Black Hole-Collisions},
year = {1986}
}
@article{Osher-Sethian-1988,
author = {Osher, S. and Sethian, J. A.},
doi = {10.1016/0021-9991(88)90002-2},
journal = {J. Comput. Phys.},
keywords = {Inverse mean curvature flow, Numerical methods, Ricci flow},
pages = {12--49},
title = {Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton--Jacobi formulations},
volume = {79},
year = {1988}
}
@incollection{Parashar00a,
address = {New York, U.S.A.},
author = {Parashar, M. and Browne, J. C.},
booktitle = {Structured Adaptive Mesh Refinement (SAMR) Grid Methods},
editor = {Baden, S. B. and Chrisochoides, N. P. and Gannon, D. B. and Norman, M. L.},
gbs_id = {Fuyr8uvG46UC},
keywords = {Finite difference methods, Numerical methods},
pages = {1--18},
publisher = {Springer},
series = {IMA Volumes in Mathematics and its Applications},
title = {System Engineering for High Performance Computing Software: The {HDDA}/{DAGH} Infrastructure for Implementation of Parallel Structured Adaptive Mesh Refinement},
volume = {117},
year = {2000}
}
@techreport{Pasch-1997:level-sets-and-curvature-flow,
address = {T{\"{u}}bingen, Germany},
author = {Pasch, E.},
cited = {9 January 2006},
keywords = {Inverse mean curvature flow, Numerical methods, Parabolic equations, Ricci flow},
number = {63},
publisher = {University of T{\"{u}}bingen},
series = {SFB 382 Reports},
title = {The level set method for the mean curvature flow on $(R^{3},g)$},
url = {http://www.uni-tuebingen.de/uni/opx/reports.html},
year = {1997}
}
@article{Petrich-Shapiro-Teukolsky-1985,
author = {Petrich, L. I. and Shapiro, S. L. and Teukolsky, S. A.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black hole formation, Collisionless matter, Dust, Gravitational collapse, Maximal slicing, Numerical relativity, Spherical symmetry},
pages = {2459--2469},
title = {Oppenheimer--Snyder Collapse with Maximal Time Slicing and Isotropic Coordinates},
volume = {31},
year = {1985}
}
@online{petsc-home-page,
author = {Balay, S. and Buschelman, K. and Gropp, W. D. and Kaushik, D. and Knepley, M. and Curfman McInnes, L. and Smith, B. F. and Zhang, H.},
cited = {9 January 2006},
format = {project homepage},
keywords = {Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods},
publisher = {Argonne National Laboratory},
title = {PETSc: Portable, Extensible Toolkit for Scientific Computation},
url = {http://www.mcs.anl.gov/petsc}
}
@techreport{petsc-manual,
address = {Argonne, U.S.A.},
author = {Balay, S. and Buschelman, K. and Gropp, W. D. and Kaushik, D. and Knepley, M. and Curfman McInnes, L. and Smith, B. F. and Zhang, H.},
cited = {20 August 2003},
keywords = {Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods},
number = {ANL-95/11 -- Revision 2.1.5},
publisher = {Argonne National Laboratory},
title = {PETSc Users Manual},
url = {http://www-unix.mcs.anl.gov/petsc/petsc-as/documentation/},
year = {2003}
}
@inproceedings{petsc-efficient,
address = {Boston, U.S.A.},
author = {Balay, S. and Gropp, W. D. and Curfman McInnes, L. and Smith, B. F.},
booktitle = {Modern Software Tools for Scientific Computing},
conference = {Proceedings of SciTools '96 Workshop held in Oslo, Norway},
editor = {Arge, E. and Bruaset, A. M. and Langtangen, H. P.},
keywords = {Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods},
pages = {163--202},
publisher = {Birkh\"auser},
title = {Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries},
year = {1997}
}
@phdthesis{Pfeiffer:thesis,
address = {Ithaca, U.S.A.},
author = {Pfeiffer, H. P.},
cited = {1 October 2006},
format = {phd},
keywords = {Black holes, Black hole angular momentum, Black hole collisions, Elliptic equations, Linear equations, Multi black hole solutions, Nonlinear algebraic equations, Numerical methods, Numerical relativity, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/0510016},
school = {Cornell University},
title = {Initial Data for Black Hole Evolutions},
year = {2003}
}
@article{Pfeiffer:2000um,
adsurl = {http://adsabs.harvard.edu/abs/2000PhRvD..62j4018P},
author = {Pfeiffer, H. P. and Teukolsky, S. A. and Cook, G. B.},
cited = {1 October 2006},
doi = {10.1103/PhysRevD.62.104018},
eid = {104018},
eprint = {gr-qc/0006084},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black hole angular momentum, Black holes, Constraint equations, Elliptic equations, Energy and momentum, Minimization, Numerical methods, Numerical relativity, Partial differential equations, Innermost stable circular orbits (ISCO)},
numpages = {11},
onlineversion = {http://arXiv.org/abs/gr-qc/0006084},
title = {Quasicircular orbits for spinning binary black holes},
volume = {62},
year = {2000}
}
@article{Pfeiffer:2002wt,
adsurl = {http://adsabs.harvard.edu/abs/2003CoPhC.152..253P},
author = {Pfeiffer, H. P. and Kidder, L. E. and Scheel, M. A. and Teukolsky, S. A.},
cited = {9 January 2006},
doi = {10.1016/S0010-4655(02)00847-0},
journal = {Comput. Phys. Commun.},
keywords = {Black holes, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/0202096},
pages = {253--273},
title = {A multidomain spectral method for solving elliptic equations},
volume = {152},
year = {2003}
}
@article{Pfeiffer:2002xz,
adsurl = {http://adsabs.harvard.edu/abs/2002PhRvD..66b4047P},
author = {Pfeiffer, H. P. and Cook, G. B. and Teukolsky, S. A.},
cited = {1 October 2006},
doi = {10.1103/PhysRevD.66.024047},
eid = {024047},
journal = {Phys. Rev. D},
keywords = {ADM formalism, Black holes, Constraints, Energy and momentum, Elliptic equations, Numerical relativity, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/0203085},
pages = {1--17},
title = {Comparing initial-data sets for binary black holes},
volume = {66},
year = {2002}
}
@misc{Pfeiffer-2006-Email-to-Thornburg,
author = {Pfeiffer, H. P.},
format = {personal communication},
keywords = {Minimization, Numerical methods, Numerical relativity, Spectral methods},
year = {2006}
}
@book{Press92,
address = {Cambridge, U.K.; New York, U.S.A.},
author = {Press, W. H. and Flannery, B. P. and Teukolsky, S. A. and Vetterling, W. T.},
edition = {2nd},
gbs_id = {ruR6ds7RIpEC},
keywords = {Minimization, Nonlinear algebraic equations, Numerical methods},
publisher = {Cambridge University Press},
title = {Numerical Recipes},
year = {1992}
}
@article{Pretorius:2003wc,
adsurl = {http://adsabs.harvard.edu/abs/2004JCoPh.198...10P},
archiveprefix = {arXiv},
author = {Pretorius, F. and Lehner, L.},
cited = {9 January 2006},
doi = {10.1016/j.jcp.2004.01.001},
eprint = {gr-qc/0302003},
journal = {J. Comput. Phys.},
keywords = {Finite difference methods, Numerical methods, Numerical relativity, Partial differential equations, Scalar fields, Spherical symmetry},
onlineversion = {http://arXiv.org/abs/gr-qc/0302003},
pages = {10--34},
title = {Adaptive mesh refinement for characteristic codes},
volume = {198},
year = {2004}
}
@article{Pretorius:2005amr,
archiveprefix = {arXiv},
author = {Pretorius, F. and Choptuik, M. W.},
cited = {3 October 2006},
doi = {10.1016/j.jcp.2006.02.011},
eprint = {gr-qc/0508110},
journal = {J. Comput. Phys.},
keywords = {Elliptic equations, Finite difference methods, Hyperbolic partial differential equations, Numerical methods},
onlineversion = {http://arXiv.org/abs/gr-qc/0508110},
pages = {246--274},
primaryclass = {gr-qc},
title = {Adaptive mesh refinement for coupled elliptic-hyperbolic systems},
volume = {218},
year = {2006}
}
@article{Regge:1961px,
author = {Regge, T.},
journal = {Nuovo Cimento A},
keywords = {Approximation methods, Numerical relativity, Regge calculus},
pages = {558--571},
title = {General Relativity without Coordinates},
volume = {19},
year = {1961}
}
@book{Richtmyer-Morton-2nd-edition,
address = {Malabar, U.S.A.},
author = {Richtmyer, R. D. and Morton, K. W.},
edition = {2nd},
keywords = {Numerical methods},
note = {Reprinted second edition of 1967},
publisher = {Krieger},
title = {Difference Methods for Initial-Value Problems},
year = {1994}
}
@book{Saad-2003:iterative-methods-2nd-ed,
address = {Philadelphia, U.S.A.},
author = {Saad, Y.},
edition = {2nd},
gbs_id = {ZdLeBlqYeF8C},
keywords = {Linear equations, Numerical methods},
publisher = {SIAM},
title = {Iterative Methods for Sparse Linear Systems},
year = {2003}
}
@preprint{Schnetter02a,
author = {Schnetter, E.},
cited = {9 January 2006},
format = {arxiv},
keywords = {Apparent horizons, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity},
title = {A fast apparent horizon algorithm},
url = {http://arXiv.org/abs/gr-qc/0206003},
year = {2002}
}
@article{Schnetter03a,
author = {Schnetter, E.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/20/22/001},
journal = {Class. Quantum Grav.},
keywords = {Apparent horizons, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity},
onlineversion = {http://arXiv.org/abs/gr-qc/0306006},
pages = {4719--4737},
title = {Finding Apparent Horizons and other Two-Surfaces of Constant Expansion},
volume = {20},
year = {2003}
}
@article{Schnetter-etal-03b,
adsurl = {http://adsabs.harvard.edu/abs/2004CQGra..21.1465S},
archiveprefix = {arXiv},
author = {Schnetter, E. and Hawley, S. H. and Hawke, I.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/21/6/014},
eprint = {gr-qc/0310042},
journal = {Class. Quantum Grav.},
keywords = {Finite difference methods, Numerical methods, Numerical relativity, Partial differential equations},
onlineversion = {http://arXiv.org/abs/gr-qc/0310042},
pages = {1465--1488},
title = {Evolutions in 3-D numerical relativity using fixed mesh refinement},
volume = {21},
year = {2004}
}
@article{Schnetter04,
author = {Schnetter, E. and Herrmann, F. and Pollney, D.},
cited = {9 January 2006},
eid = {044033},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black hole collisions, Numerical methods, Numerical relativity},
onlineversion = {http://arXiv.org/abs/gr-qc/0410081},
title = {Horizon Pretracking},
volume = {71},
year = {2005}
}
@article{Schnetter-Krishnan-2005,
author = {Schnetter, E. and Krishnan, B.},
cited = {3 October 2006},
eid = {021502},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black holes, Dust, Event horizons, Horizons, Numerical relativity, Schwarzschild solution, Spherical symmetry, Trapped surfaces, Vaidya spacetime},
onlineversion = {http://arXiv.org/abs/gr-qc/0511017},
title = {Nonsymmetric trapped surfaces in the Schwarzschild Vaidya spacetimes},
volume = {73},
year = {2006}
}
@article{Schnetter-Krishnan-Beyer-2006,
author = {Schnetter, E. and Krishnan, B. and Beyer, F.},
cited = {30 October 2006},
eid = {024028},
journal = {Phys. Rev. D},
keywords = {Angular momentum, Apparent horizons, Area increase law, Axisymmetric black holes, Black hole angular momentum, Black hole collisions, Black holes, Distorted black holes, Dynamical horizons, Finite difference methods, Horizon geometry, Isolated horizons, Kerr black holes, Killing field, Multi black hole spacetimes, Multipole expansions, Quasi-local angular momentum, Quasi-local black holes, Quasi-local energy-momentum, Quasi-local mass, Rotating black holes, Three-manifolds, Trapped surfaces},
onlineversion = {http://arXiv.org/abs/gr-qc/0604015},
title = {Introduction to Dynamical Horizons in numerical relativity},
volume = {74},
year = {2006}
}
@book{Schroeder86,
address = {Berlin, Germany; New York, U.S.A.},
author = {Schroeder, M. R.},
edition = {2nd},
keywords = {no keywords},
publisher = {Springer},
series = {Springer Series in Information Sciences},
title = {Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity},
volume = {7},
year = {1986}
}
@article{Seidel92a,
author = {Seidel, E. and Suen, W.-M.},
doi = {10.1103/PhysRevLett.69.1845},
journal = {Phys. Rev. Lett.},
keywords = {Apparent horizons, Black holes, Boundary conditions, Excision, Finite difference methods, Horizons, Numerical methods, Numerical relativity, Spherical symmetry},
pages = {1845--1848},
title = {Towards a Singularity-Proof Scheme in Numerical Relativity},
volume = {69},
year = {1992}
}
@book{Shampine-Gordon-1975,
address = {San Francisco, U.S.A.},
author = {Shampine, L. F. and Gordon, M. K.},
keywords = {Finite difference methods, Numerical methods, Ordinary differential equations},
publisher = {W.H. Freeman},
title = {Computer solution of Ordinary Differential Equations},
year = {1975}
}
@article{Shapiro79z,
adsurl = {http://adsabs.harvard.edu/abs/1979ApJ...234L.177S},
author = {Shapiro, S. L. and Teukolsky, S. A.},
doi = {10.1086/183134},
journal = {Astrophys. J. Lett.},
keywords = {Apparent horizons, Black hole formation, Black holes, Event horizons, Geodesics, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Relativistic fluid dynamics, Spherical symmetry},
pages = {L177--L181},
title = {Gravitational Collapse of Supermassive Stars to Black Holes: Numerical Solution of the Einstein Equations},
volume = {234},
year = {1979}
}
@article{Shapiro80,
adsurl = {http://adsabs.harvard.edu/abs/1980ApJ...235..199S},
author = {Shapiro, S. L. and Teukolsky, S. A.},
doi = {10.1086/157625},
journal = {Astrophys. J.},
keywords = {Apparent horizons, Black hole formation, Black holes, Event horizons, Geodesics, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Relativistic fluid dynamics, Spherical symmetry},
pages = {199--215},
title = {Gravitational Collapse to Neutron Stars and Black Holes: Computer Generation of Spherical Spacetimes},
volume = {235},
year = {1980}
}
@article{Shapiro85:partI,
author = {Shapiro, S. L. and Teukolsky, S. A.},
doi = {10.1086/163587},
journal = {Astrophys. J.},
keywords = {Apparent horizons, Black hole formation, Black holes, Collisionless matter, Dust, Event horizons, Geodesics, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Spherical symmetry},
pages = {34--57},
title = {Relativistic stellar dynamics on the computer. I. Motivation and Numerical Method},
volume = {298},
year = {1985}
}
@article{Shapiro85,
author = {Shapiro, S. L. and Teukolsky, S. A.},
doi = {10.1086/163588},
journal = {Astrophys. J.},
keywords = {Apparent horizons, Black hole formation, Black holes, Collisionless matter, Dust, Event horizons, Geodesics, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Spherical symmetry},
pages = {58--79},
title = {Relativistic stellar dynamics on the computer: II. Physical applications},
volume = {298},
year = {1985}
}
@article{Shapiro92a,
author = {Shapiro, S. L. and Teukolsky, S. A.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Black hole collisions, Black hole formation, Collisionless matter, Dust, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Ordinary differential equations},
pages = {2739--2750},
title = {Collision of relativistic clusters and the formation of black holes},
volume = {45},
year = {1992}
}
@article{Shibata97a,
author = {Shibata, M.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Elliptic equations, Nonlinear algebraic equations, Linear equations, Numerical methods, Numerical relativity},
pages = {2002--2013},
title = {Apparent horizon finder for a special family of spacetimes in 3D numerical relativity},
volume = {55},
year = {1997}
}
@article{Shibata-Uryu-2000b,
author = {Shibata, M. and Ury{\={u}}, K.},
eid = {087501},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Elliptic equations, Nonlinear algebraic equations, Linear equations, Numerical methods, Numerical relativity},
title = {Apparent Horizon Finder for General Three-Dimensional Spaces},
volume = {62},
year = {2000}
}
@phdthesis{Shoemaker99,
address = {Austin, U.S.A.},
author = {Shoemaker, D. M.},
format = {phd},
keywords = {Apparent horizons, Inverse mean curvature flow, Multi black hole spacetimes, Numerical methods, Numerical relativity, Ricci flow, Topology change},
school = {The University of Texas at Austin},
title = {Apparent Horizons in Binary Black Hole Spacetimes},
year = {1999}
}
@article{Shoemaker-Huq-Matzner-2000,
author = {Shoemaker, D. M. and Huq, M. F. and Matzner, R. A.},
cited = {9 January 2006},
eid = {124005},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Inverse mean curvature flow, Multi black hole spacetimes, Numerical methods, Numerical relativity, Ricci flow, Topology change},
onlineversion = {http://arXiv.org/abs/gr-qc/0006042},
title = {Generic tracking of multiple apparent horizons with level flow},
volume = {62},
year = {2000}
}
@book{Stoer-Bulirsch-1980,
address = {Berlin, Germany; New York, U.S.A.},
author = {Stoer, J. and Bulirsch, R.},
keywords = {Numerical methods},
publisher = {Springer},
title = {Introduction to Numerical Analysis},
year = {1980}
}
@article{Szilagyi-etal-2006a,
adsurl = {http://adsabs.harvard.edu/abs/2007CQGra..24S.275S},
archiveprefix = {arXiv},
author = {Szil{\'{a}}gyi, B. and Pollney, D. and Rezzolla, L. and Thornburg, J. and Winicour, J.},
cited = {9 April 2007},
doi = {10.1088/0264-9381/24/12/S18},
eprint = {gr-qc/0612150},
journal = {Class. Quantum Grav.},
keywords = {Apparent horizons, Black hole collisions, Black holes, Constraints, Distorted black holes, Excision, Finite difference methods, Harmonic coordinates, Harmonic gauge, Multi black hole spacetimes, Numerical relativity, Rotating black holes, Vacuum Einstein equations, Wave equation},
pages = {S275--S293},
primaryclass = {gr-qc},
title = {An explicit harmonic code for black-hole evolution using excision},
volume = {24},
year = {2007}
}
@article{Teukolsky00,
archiveprefix = {arXiv},
author = {Teukolsky, S. A.},
doi = {10.1103/PhysRevD.61.087501},
eid = {087501},
eprint = {gr-qc/9909026},
journal = {Phys. Rev. D},
keywords = {Finite difference methods, Numerical methods, Partial differential equations},
primaryclass = {gr-qc},
title = {Stability of the iterated Crank-Nicholson method in numerical relativity},
volume = {61},
year = {2000}
}
@article{Thornburg95,
author = {Thornburg, J.},
cited = {9 January 2006},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity},
onlineversion = {http://arXiv.org/abs/gr-qc/9508014},
pages = {4899--4918},
title = {Finding apparent horizons in numerical relativity},
volume = {54},
year = {1996}
}
@article{Thornburg98,
author = {Thornburg, J.},
cited = {9 January 2006},
eid = {104007},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black holes, Constraints, Numerical methods, Numerical relativity, Scalar fields, Spherical symmetry},
onlineversion = {http://arXiv.org/abs/gr-qc/9801087},
title = {A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes -- I: Initial Data},
volume = {59},
year = {1999}
}
@preprint{Thornburg99,
author = {Thornburg, J.},
cited = {9 January 2006},
format = {arxiv},
keywords = {Apparent horizons, Black holes, Initial boundary value problem, Numerical methods, Numerical relativity, Scalar fields, Spherical symmetry},
title = {A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes -- II: Time Evolution},
url = {http://arXiv.org/abs/gr-qc/9906022},
year = {1999}
}
@article{Thornburg2003:AH-finding,
adsurl = {http://adsabs.harvard.edu/abs/2004CQGra..21..743T},
archiveprefix = {arXiv},
author = {Thornburg, J.},
cited = {9 January 2006},
doi = {10.1088/0264-9381/21/2/026},
eprint = {gr-qc/0306056},
journal = {Class. Quantum Grav.},
keywords = {Apparent horizons, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity},
onlineversion = {http://arXiv.org/abs/gr-qc/0306056},
pages = {743--766},
title = {A fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity},
volume = {21},
year = {2004}
}
@article{Tod91,
author = {Tod, K. P.},
journal = {Class. Quantum Grav.},
keywords = {Apparent horizons, Inverse mean curvature flow, Ricci flow, Trapped surfaces},
pages = {L115--L118},
title = {Looking for marginally trapped surfaces},
volume = {8},
year = {1991}
}
@book{Trottenberg-Oosterlee-Schueller-2001:multigrid,
address = {San Diego, U.S.A.},
author = {Trottenberg, U. and Oosterlee, C. W. and Sch{\"{u}}ller, A.},
gbs_id = {-og1wD-Nx{\_}wC},
keywords = {Elliptic equations, Linear equations, Numerical methods},
publisher = {Academic Press},
title = {Multigrid},
year = {2001}
}
@online{UMFPACK-author-and-web-site,
author = {Davis, T. A.},
cited = {6 January 2007},
format = {project homepage},
keywords = {Linear equations, Numerical methods},
publisher = {University of Florida (CISE)},
title = {UMFPACK: unsymmetric multifrontal sparse LU factorization package},
url = {http://www.cise.ufl.edu/research/sparse/umfpack/}
}
@book{Wald84,
address = {Chicago},
adsurl = {http://adsabs.harvard.edu/abs/1984ucp..book.....W},
author = {Wald, R. M.},
gbs_id = {IdAwZ1ei1scC},
keywords = {ADM formalism},
publisher = {University of Chicago Press},
title = {General Relativity},
year = {1984}
}
@article{Wald91,
author = {Wald, R. M. and Iyer, V.},
journal = {Phys. Rev. D},
keywords = {Black holes, Cosmic censorship, Foliations, Naked singularities, Schwarzschild solution, Spherical symmetry, Trapped surfaces},
pages = {R3719--R3722},
title = {Trapped surfaces in the Schwarzschild geometry and cosmic censorship},
volume = {44},
year = {1991}
}
@phdthesis{Walker98a,
address = {Urbana, U.S.A.},
author = {Walker, P.},
format = {phd},
keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Distorted black holes, Event horizons, Excision, Finite difference methods, Hyperbolic partial differential equations, Multi black hole spacetimes, Null surfaces, Numerical methods, Numerical relativity, Rotating black holes, Spherical symmetry},
school = {University of Illinois at Urbana-Champaign},
title = {Horizons, Hyperbolic Systems, and Inner Boundary Conditions in Numerical Relativity},
year = {1998}
}
@inproceedings{York79,
address = {Cambridge; New York},
adsurl = {http://adsabs.harvard.edu/abs/1979sgrr.work...83Y},
author = {York Jr, J. W.},
booktitle = {Sources of Gravitational Radiation},
conference = {Proceedings of the Battelle Seattle Workshop, July 24\,--\,August 4, 1978},
editor = {Smarr, L. L.},
gbs_id = {rJBOAAAAIAAJ{\&}pg=PA83},
keywords = {ADM formalism, Cauchy problem, Constraint equations},
pages = {83--126},
publisher = {Cambridge University Press},
title = {Kinematics and Dynamics of General Relativity},
year = {1979}
}
@inproceedings{York89,
address = {Cambridge, U.K.; New York, U.S.A.},
author = {York Jr, J. W.},
booktitle = {Frontiers in Numerical Relativity},
conference = {Proceedings of the International Workshop on Numerical Relativity, University of Illinois at Urbana-Champaign, U.S.A., May 9\,--\,13, 1988},
editor = {Evans, C. R. and Finn, L. S. and Hobill, D. W.},
keywords = {ADM formalism, Apparent horizons, Cauchy problem, Constraint equations},
pages = {89--109},
publisher = {Cambridge University Press},
title = {Initial Data for Collisions of Black Holes and Other Gravitational Miscellany},
year = {1989}
}