1 Abrahams, A.M., Cook, G.B., Shapiro, S.L., and Teukolsky, S.A., “Solving Einstein’s Equations for Rotating Spacetimes: Evolution of Relativistic Star Clusters”, Phys. Rev. D, 49, 5153–5164, (1994).
2 Abrahams, A.M., and Evans, C.R., “Trapping a Geon: Black Hole Formation by an Imploding Gravitational Wave”, Phys. Rev. D, 46, R4117–R4121, (1992).
3 Abrahams, A.M., Heiderich, K.H., Shapiro, S.L., and Teukolsky, S.A., “Vacuum initial data, singularities, and cosmic censorship”, Phys. Rev. D, 46, 2452–2463, (1992).
4 Alcubierre, M., Brandt, S., Brügmann, B., Gundlach, C., Massó, J., Seidel, E., and Walker, P., “Test-beds and applications for apparent horizon finders in numerical relativity”, Class. Quantum Grav., 17, 2159–2190, (2000). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9809004.
5 Alcubierre, M., Brügmann, B., Diener, P., Guzmán, F.S., Hawke, I., Hawley, S., Herrmann, F., Koppitz, M., Pollney, D., Seidel, E., and Thornburg, J., “Dynamical evolution of quasi-circular binary black hole data”, Phys. Rev. D, 72, 044004, (2005). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0411149.
6 Andersson, L., and Metzger, J., personal communication, (2007). Personal communication from Lars Andersson to Bela Szilágyi.
7 Anninos, P., Bernstein, D., Brandt, S., Libson, J., Massó, J., Seidel, E., Smarr, L.L., Suen, W.-M., and Walker, P., “Dynamics of Apparent and Event Horizons”, Phys. Rev. Lett., 74, 630–633, (1995). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9403011.
8 Anninos, P., Camarda, K., Libson, J., Massó, J., Seidel, E., and Suen, W.-M., “Finding apparent horizons in dynamic 3D numerical spacetimes”, Phys. Rev. D, 58, 024003, 1–12, (1998).
9 Anninos, P., Daues, G., Massó, J., Seidel, E., and Suen, W.-M., “Horizon boundary conditions for black hole spacetimes”, Phys. Rev. D, 51, 5562–5578, (1995).
10 Ansorg, M., “A double-domain spectral method for black hole excision data”, Phys. Rev. D, 72, 024018, 1–10, (2005). Related online version (cited on 30 January 2007):
External Linkhttp://arxiv.org/abs/gr-qc/0505059.
11 Ansorg, M., Brügmann, B., and Tichy, W., “Single-domain spectral method for black hole puncture data”, Phys. Rev. D, 70, 064011, 1–13, (2004). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0404056.
12 Ansorg, M., Kleinwächter, A., and Meinel, R., “Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods”, Astron. Astrophys., 405, 711–721, (2003). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/astro-ph/0301173.
13 Ansorg, M., and Petroff, D., “Black holes surrounded by uniformly rotating rings”, Phys. Rev. D, 72, 024019, (2005). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0505060.
14 Arnowitt, R., Deser, S., and Misner, C.W., “The dynamics of general relativity”, in Witten, L., ed., Gravitation: An Introduction to Current Research, 227–265, (Wiley, New York, U.S.A., 1962). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0405109.
15 Ascher, U.M., Mattheij, R.M.M., and Russell, R.D., Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, (Prentice-Hall, Englewood Cliffs, U.S.A., 1988).
16 Ashtekar, A., Beetle, C., and Fairhurst, S., “Isolated horizons: a generalization of black hole mechanics”, Class. Quantum Grav., 16, L1–L7, (1999). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9812065.
17 Ashtekar, A., and Galloway, G., “Some uniqueness results for dynamical horizons”, Adv. Theor. Math. Phys., 9, 1–30, (2005). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0503109.
18 Ashtekar, A., and Krishnan, B., “Dynamical Horizons: Energy, Angular Momentum, Fluxes, and Balance Laws”, Phys. Rev. Lett., 89, 261101, 1–4, (2002). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0207080.
19 Ashtekar, A., and Krishnan, B., “Dynamical horizons and their properties”, Phys. Rev. D, 68, 104030, 1–25, (2003). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0308033.
20 Ashtekar, A., and Krishnan, B., “Isolated and Dynamical Horizons and Their Applications”, Living Rev. Relativity, 7, lrr-2004-10, 10, (2004). URL (cited on 09 January 2006):
http://www.livingreviews.org/lrr-2004-10.
21 Baiotti, L., Hawke, I., Montero, P.J., Löffler, F., Rezzolla, L., Stergioulas, N., Font, J.A., and Seidel, E., “Three-dimensional relativistic simulations of rotating neutron star collapse to a Kerr black hole”, Phys. Rev. D, 71, 024035, (2005). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0403029.
22 Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M., Curfman McInnes, L., Smith, B.F., and Zhang, H., “PETSc: Portable, Extensible Toolkit for Scientific Computation”, project homepage, Argonne National Laboratory. URL (cited on 09 January 2006):
External Linkhttp://www.mcs.anl.gov/petsc.
23 Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M., Curfman McInnes, L., Smith, B.F., and Zhang, H., PETSc Users Manual, ANL-95/11 – Revision 2.1.5, (Argonne National Laboratory, Argonne, U.S.A., 2003). URL (cited on 20 August 2003):
External Linkhttp://www-unix.mcs.anl.gov/petsc/petsc-as/documentation/.
24 Balay, S., Gropp, W.D., Curfman McInnes, L., and Smith, B.F., “Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries”, in Arge, E., Bruaset, A.M., and Langtangen, H.P., eds., Modern Software Tools for Scientific Computing, Proceedings of SciTools ’96 Workshop held in Oslo, Norway, 163–202, (Birkhäuser, Boston, U.S.A., 1997).
25 Bartnik, R., personal communication. Personal communication from Robert Bartnik to Carsten Gundlach.
26 Baumgarte, T.W., Cook, G.B., Scheel, M.A., Shapiro, S.L., and Teukolsky, S.A., “Implementing an apparent-horizon finder in three dimensions”, Phys. Rev. D, 54, 4849–4857, (1996). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9606010.
27 Baumgarte, T.W., and Shapiro, S.L., “Numerical relativity and compact binaries”, Phys. Rep., 376, 41–131, (2003). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0211028.
28 Bernstein, D., Notes on the Mean Curvature Flow Method for Finding Apparent Horizons, (National Center for Supercomputing Applications, Urbana-Champaign, U.S.A., 1993).
29 Bishop, N.T., “The Closed Trapped Region and the Apparent Horizon of Two Schwarzschild Black Holes”, Gen. Relativ. Gravit., 14, 717–723, (1982).
30 Bishop, N.T., “The horizons of two Schwarzschild black holes”, Gen. Relativ. Gravit., 16, 589–593, (1984).
31 Bishop, N.T., “The Event Horizons of Two Schwarzschild black holes”, Gen. Relativ. Gravit., 20, 573–581, (1988).
32 Bizoń, P., Malec, E., and Ó Murchadha, N., “Trapped Surfaces in Spherical Stars”, Phys. Rev. Lett., 61, 1147–1150, (1988).
33 Bonazzola, S., Frieben, J., Gourgoulhon, E., and Marck, J.-A., “Spectral methods in general relativity – toward the simulation of 3D-gravitational collapse of neutron stars”, in Ilin, A.V., and Scott, L.R., eds., ICOSAHOM ’95, Proceedings of the Third International Conference on Spectral and High Order Methods: Houston, Texas, June 5 – 9, 1995, Houston Journal of Mathematics, 3–19, (University of Houston, Houston, U.S.A., 1996). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9604029.
34 Bonazzola, S., Gourgoulhon, E., and Marck, J.-A., “Spectral methods in general relativistic astrophysics”, J. Comput. Appl. Math., 109, 433–473, (1999). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9811089.
35 Bonazzola, S., and Marck, J.-A., “Pseudo-Spectral Methods Applied to Gravitational Collapse”, in Evans, C.R., Finn, L.S., and Hobill, D.W., eds., Frontiers in Numerical Relativity, Proceedings of the International Workshop on Numerical Relativity, University of Illinois at Urbana-Champaign, USA, May 9 – 13, 1988, 239–253, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1989).
36 Booth, I., “Black hole boundaries”, Can. J. Phys., 83, 1073–1099, (2005). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0508107.
37 Boyd, J.P., Chebyshev and Fourier Spectral Methods, (Dover Publications, Mineola, U.S.A., 2001), 2nd edition.
38 Brankin, R.W., Gladwell, I., and Shampine, L.F., “RKSUITE: A Suite of Runge–Kutta Codes for the Initial Value Problem for ODEs”, other, Dept. of Mathematics, Southern Methodist University, Dallas, TX, (1992). URL (cited on 09 January 2006):
External Linkhttp://www.netlib.org/ode/rksuite/.
39 Brent, R.P., Algorithms for Minimization Without Derivatives, (Dover Publications, Mineola, U.S.A., 2002). Reprint of 1973 original edition.
40 Brewin, L.C., “Is the Regge Calculus a Consistent Approximation to General Relativity?”, Gen. Relativ. Gravit., 32, 897–918, (2000). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9502043.
41 Brewin, L.C., and Gentle, A.P., “On the Convergence of Regge Calculus to General Relativity”, Class. Quantum Grav., 18, 517–525, (2001). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0006017.
42 Briggs, W.L., Henson, V.E., and McCormick, S.F., A Multigrid Tutorial, (SIAM, Philadelphia, U.S.A., 2000), 2nd edition.
43 Brill, D.R., and Lindquist, R.W., “Interaction Energy in Geometrostatics”, Phys. Rev., 131, 471–476, (1963).
44 Caveny, S.A., Tracking Black Holes in Numerical Relativity: Foundations and Applications, Ph.D. Thesis, (University of Texas at Austin, Austin, U.S.A., 2002).
45 Caveny, S.A., Anderson, M., and Matzner, R.A., “Tracking Black Holes in Numerical Relativity”, Phys. Rev. D, 68, 104009, (2003). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0303099.
46 Caveny, S.A., and Matzner, R.A., “Adaptive event horizon tracking and critical phenomena in binary black hole coalescence”, Phys. Rev. D, 68, 104003–1–13, (2003). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0303109.
47 Choptuik, M.W., A Study of Numerical Techniques for Radiative Problems in General Relativity, Ph.D. Thesis, (University of British Columbia, Vancouver, Canada, 1986).
48 Choptuik, M.W., “Experiences with an Adaptive Mesh Refinement Algorithm in Numerical Relativity”, in Evans, C.R., Finn, L.S., and Hobill, D.W., eds., Frontiers in Numerical Relativity, Proceedings of the International Workshop on Numerical Relativity, University of Illinois at Urbana-Champaign (Urbana-Champaign, Illinois, USA), May 9 – 13, 1988, 206–221, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1989).
49 Chruściel, P.T., and Galloway, G.J., “Horizons Non-Differentiable on a Dense Set”, Commun. Math. Phys., 193, 449–470, (1998). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9611032.
50 Cook, G.B., Initial Data for the Two-Body Problem of General Relativity, Ph.D. Thesis, (University of North Carolina at Chapel Hill, Chapel Hill, U.S.A., 1990).
51 Cook, G.B., and Abrahams, A.M., “Horizon Structure of Initial-Data Sets for Axisymmetric Two-Black-Hole Collisions”, Phys. Rev. D, 46, 702–713, (1992).
52 Cook, G.B., and York Jr, J.W., “Apparent Horizons for Boosted or Spinning Black Holes”, Phys. Rev. D, 41, 1077–1085, (1990).
53 Curtis, A.R., and Reid, J.K., “The Choice of Step Lengths When Using Differences to Approximate Jacobian Matrices”, J. Inst. Math. Appl., 13, 121–126, (1974).
54 Davis, T.A., “UMFPACK: unsymmetric multifrontal sparse LU factorization package”, project homepage, University of Florida (CISE). URL (cited on 6 January 2007):
External Linkhttp://www.cise.ufl.edu/research/sparse/umfpack/.
55 Davis, T.A., “Algorithm 832: UMFPACK V4.3—an unsymmetric-pattern multifrontal method”, ACM Trans. Math. Software, 30, 196–199, (2004). Related online version (cited on 09 January 2006):
External Linkhttp://www.cise.ufl.edu/~davis/. TR-02-002.
56 Davis, T.A., “A column pre-ordering strategy for the unsymmetric-pattern multifrontal method”, ACM Trans. Math. Software, 30, 165–195, (2004). Related online version (cited on 09 January 2006):
External Linkhttp://www.cise.ufl.edu/~davis/. TR-02-001.
57 Davis, T.A., and Duff, I.S., “An unsymmetric-pattern multifrontal method for sparse LU factorization”, SIAM J. Matrix Anal. Appl., 18, 140–158, (1997).
58 Davis, T.A., and Duff, I.S., “A combined unifrontal/multifrontal method for unsymmetric sparse matrices”, ACM Trans. Math. Software, 25, 1–19, (1999).
59 Dennis Jr, J.E., and Schnabel, R.B., Numerical Methods for Unconstrained Optimization and Nonlinear Equations, (SIAM, Philadelphia, U.S.A., 1996).
60 Diener, P., “A New General Purpose Event Horizon Finder for 3D”, Class. Quantum Grav., 20, 4901–4917, (2003). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0305039.
61 Diener, P., personal communication, (2007).
62 Diener, P., Herrmann, F., Pollney, D., Schnetter, E., Seidel, E., Takahashi, R., Thornburg, J., and Ventrella, J., “Accurate Evolution of Orbiting Binary Black Holes”, Phys. Rev. Lett., 96, 121101, (2006). Related online version (cited on 3 October 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0512108.
63 Dreyer, O., Krishnan, B., Schnetter, E., and Shoemaker, D., “Introduction to isolated horizons in numerical relativity”, Phys. Rev. D, 67, 024018, 1–14, (2003). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0206008.
64 Du Fort, E.C., and Frankel, S.P., “Stability Conditions in the Numerical Treatment of Parabolic Differential Equations”, Math. Tables Aids Comput., 7, 135–152, (1953).
65 Duff, I.S., Erisman, A.M., and Reid, J.K., Direct Methods for Sparse Matrices, (Oxford University Press, Oxford, U.K.; New York, U.S.A., 1986).
66 Dykema, P.G., The Numerical Simulation of Axially Symmetric Gravitational Collapse, Ph.D. Thesis, (University of Texas at Austin, Austin, U.S.A., 1980).
67 Eardley, D.M., “Gravitational Collapse of Marginally Bound Spheroids: Initial Conditions”, Phys. Rev. D, 12, 3072–3076, (1975).
68 Eppley, K.R., The numerical evolution of the collision of two black holes, Ph.D. Thesis, (Princeton University, Princeton, U.S.A., 1975).
69 Eppley, K.R., “Evolution of time-symmetric gravitational waves: Initial data and apparent horizons”, Phys. Rev. D, 16, 1609–1614, (1977).
70 Fornberg, B., A Practical Guide to Pseudospectral Methods, Cambridge Monographs on Applied and Computational Mathematics, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1998).
71 Forsythe, G.E., Malcolm, M.A., and Moler, C.B., Computer Methods for Mathematical Computations, (Prentice-Hall, Englewood Cliffs, U.S.A., 1977). Related online version (cited on 09 January 2006):
External Linkhttp://www.netlib.org/fmm/.
72 Gentle, A.P., “Regge Calculus: A Unique Tool for Numerical Relativity”, Gen. Relativ. Gravit., 34, 1701–1718, (2002). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0408006.
73 Gentle, A.P., and Miller, W.A., “A fully (3+1)-dimensional Regge calculus model of the Kasner cosmology”, Class. Quantum Grav., 15, 389–405, (1998). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9706034.
74 Goodale, T., Allen, G., Lanfermann, G., Massó, J., Radke, T., Seidel, E., and Shalf, J., “The Cactus Framework and Toolkit: Design and Applications”, in Palma, J.M.L.M.and Dongarra, J., Hernández, V., and Sousa, A.A., eds., High Performance Computing for Computational Science (VECPAR 2002), 5th International Conference, Porto, Portugal, June 26 – 28, 2002: Selected papers and invited talks, vol. 2565 of Lecture Notes in Computer Science, 197–227, (Springer, Berlin, Germany; New York, U.S.A., 2003).
75 Gottlieb, D., and Orszag, S.A., Numerical Analysis of Spectral Methods: Theory and Applications, vol. 26 of Regional Conference Series in Applied Mathematics, (SIAM, Philadelphia, U.S.A., 1977). Based on a series of lectures presented at the NSF-CBMS regional conference held at Old Dominion University from August 2 – 6, 1976.
76 Gourgoulhon, E., and Jaramillo, J.L., “A 3+1 perspective on null hypersurfaces and isolated horizons”, Phys. Rep., 423, 159–294, (2006). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0503113.
77 Grandclément, P., Bonazzola, S., Gourgoulhon, E., and Marck, J.-A., “A Multidomain Spectral Method for Scalar and Vectorial Poisson Equations with Noncompact Sources”, J. Comput. Phys., 170, 231–260, (2001). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0003072.
78 Grandclément, P., Gourgoulhon, E., and Bonazzola, S., “Binary black holes in circular orbits. II. Numerical methods and first results”, Phys. Rev. D, 65, 044021, 1–18, (2002). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0106016.
79 Grayson, M.A., “The Heat Equation Shrinks Embedded Plane Curves to Round Points”, J. Differ. Geom., 26, 285–314, (1987).
80 Gundlach, C., “Pseudo-spectral apparent horizon finders: An efficient new algorithm”, Phys. Rev. D, 57, 863–875, (1998). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9707050.
81 Hawking, S.W., “The Event Horizon”, in DeWitt, C., and DeWitt, B.S., eds., Black Holes, Based on lectures given at the 23rd session of the Summer School of Les Houches, 1972, 1–56, (Gordon and Breach, New York, U.S.A., 1973).
82 Hawking, S.W., and Ellis, G.F.R., The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics, (Cambridge University Press, Cambridge, U.K., 1973).
83 Hayward, S.A., “General laws of black hole dynamics”, Phys. Rev. D, 49, 6467–6474, (1994). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9306006.
84 Hindmarsh, A.C., “ODEPACK, A Systematized Collection of ODE Solvers”, in Stepleman, R.S. et al., ed., Scientific Computing: Applications of Mathematics and Computing to the Physical Sciences, Based on papers presented at the Tenth IMACS World Congress on System Simulation and Scientific Computation, held in Montreal, Canada, August 8 – 13, 1982, vol. 1 of IMACS Transactions on Scientific Computing, 55–64, (North-Holland, Amsterdam, Netherlands; New York, U.S.A., 1983). Related online version (cited on 09 January 2006):
External Linkhttp://www.netlib.org/odepack/index.html.
85 Hochbruck, M., Lubich, C., and Selhofer, H., “Exponential Integrators for Large Systems of Differential Equations”, SIAM J. Sci. Comput., 19, 1552–1574, (1998).
86 Hornung, R.D., and Kohn, S.R., “Managing application complexity in the SAMRAI object-oriented framework”, Concurr. Comput. Pract. Exp., 14, 347–368, (2002).
87 Hornung, R.D., Wissink, A.M., and Kohn, S.R., “Managing complex data and geometry in parallel structured AMR applications”, Eng. Comput., 22, 181–195, (2006).
88 Hughes, S.A., Keeton II, C.R., Walker, P., Walsh, K.T., Shapiro, S.L., and Teukolsky, S.A., “Finding Black Holes in Numerical Spacetimes”, Phys. Rev. D, 49, 4004–4015, (1994).
89 Huq, M.F., Apparent Horizon Location in Numerical Spacetimes, Ph.D. Thesis, (The University of Texas at Austin, Austin, U.S.A., 1996).
90 Huq, M.F., Choptuik, M.W., and Matzner, R.A., “Locating Boosted Kerr and Schwarzschild Apparent Horizons”, Phys. Rev. D, 66, 084024, (2002). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0002076.
91 Husa, S., and Winicour, J., “Asymmetric merger of black holes”, Phys. Rev. D, 60, 084019, 1–13, (1999). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9905039.
92 Kahaner, D., Moler, C.B., and Nash, S., Numerical Methods and Software, (Prentice Hall, Englewood Cliffs, U.S.A., 1989). Revised and (greatly) expanded edition of Forsythe, G.E. and Malcolm, M.A. and Moler, C.B, “Computer methods for mathematical computations”(1977).
93 Kemball, A.J., and Bishop, N.T., “The numerical determination of apparent horizons”, Class. Quantum Grav., 8, 1361–1367, (1991).
94 Kershaw, D.S., “The Incomplete Cholesky-Conjugate Gradient Method for Interative Solution of Linear Equations”, J. Comput. Phys., 26, 43–65, (1978).
95 Kidder, L.E., and Finn, L.S., “Spectral Methods for Numerical Relativity. The Initial Data Problem”, Phys. Rev. D, 62, 084026, (2000). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9911014.
96 Kidder, L.E., Scheel, M.A., Teukolsky, S.A., Carlson, E.D., and Cook, G.B., “Black hole evolution by spectral methods”, Phys. Rev. D, 62, 084032, (2000). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0005056.
97 Kidder, L.E., Scheel, M.A., Teukolsky, S.A., and Cook, G.B., “Spectral Evolution of Einstein’s Equations”, 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, conference paper, (2000).
98 Kriele, M., and Hayward, S.A., “Outer trapped surfaces and their apparent horizon”, J. Math. Phys., 38, 1593–1604, (1997).
99 Lehner, L., Bishop, N.T., Gómez, R., Szilágyi, B., and Winicour, J., “Exact solutions for the intrinsic geometry of black hole coalescence”, Phys. Rev. D, 60, 044005, 1–10, (1999).
100 Lehner, L., Gómez, R., Husa, S., Szilágyi, B., Bishop, N.T., and Winicour, J., “Bagels Form When Black Holes Collide”, institutional homepage, Pittsburgh Supercomputing Center. URL (cited on 09 January 2006):
External Linkhttp://www.psc.edu/research/graphics/gallery/winicour.html.
101 Leiler, G., and Rezzolla, L., “On the iterated Crank–Nicolson method for hyperbolic and parabolic equations in numerical relativity”, Phys. Rev. D, 73, 044001, (2006). Related online version (cited on 3 October 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0601139.
102 Libson, J., Massó, J., Seidel, E., and Suen, W.-M., “A 3D Apparent Horizon Finder”, in Jantzen, R.T., and Keiser, G.M., eds., The Seventh Marcel Grossmann Meeting: On recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories, Proceedings of the meeting held at Stanford University, July 24 – 30, 1994, 631, (World Scientific, Singapore; River Edge, U.S.A., 1996).
103 Libson, J., Massó, J., Seidel, E., Suen, W.-M., and Walker, P., “Event horizons in numerical relativity: Methods and tests”, Phys. Rev. D, 53, 4335–4350, (1996).
104 Lin, L.-M., and Novak, J., “Three-dimensional apparent horizon finder in LORENE”, personal communication, (2006). Personal communication from Lap-Ming Lin to Jonathan Thornburg.
105 Lorensen, W.E., and Cline, H.E., “Marching cubes: A high resolution 3D surface construction algorithm”, SIGGRAPH Comput. Graph., 21, 163–169, (1987).
106 MacNeice, P., Olson, K.M., Mobarry, C., de Fainchtein, R., and Packer, C., “PARAMESH: A parallel adaptive mesh refinement community toolkit”, Computer Phys. Commun., 126, 330–354, (2000).
107 Madderom, P., “Incomplete LU-Decomposition – Conjugate Gradient”, unknown format, (1984). Fortran 66 subroutine.
108 Matzner, R.A., Seidel, E., Shapiro, S.L., Smarr, L.L., Suen, W.-M., Teukolsky, S.A., and Winicour, J., “Geometry of a Black Hole Collision”, Science, 270, 941–947, (1995).
109 Metzger, J., “Numerical computation of constant mean curvature surfaces using finite elements”, Class. Quantum Grav., 21, 4625–4646, (2004). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0408059.
110 Miller, M.A., “Regge Calculus as a Fourth Order Method in Numerical Relativity”, Class. Quantum Grav., 12, 3037–3051, (1995). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9502044.
111 Misner, C.W., and Sharp, D.H., “Relativistic Equations for Adiabatic, Spherically Symmetric Gravitational Collapse”, Phys. Rev., 136, B571–B576, (1964).
112 Misner, C.W., Thorne, K.S., and Wheeler, J.A., Gravitation, (W.H. Freeman, San Francisco, U.S.A., 1973).
113 Nakamura, T., Kojima, Y., and Oohara, K., “A Method of Determining Apparent Horizons in Three-Dimensional Numerical Relativity”, Phys. Lett. A, 106, 235–238, (1984).
114 Oohara, K., “Apparent Horizon of Initial Data for Black Hole-Collisions”, in Sato, H., and Nakamura, T., eds., Gravitational Collapse and Relativity, Proceedings of Yamada Conference XIV, Kyoto International Conference Hall, Japan, April 7 – 11, 1986, 313–319, (World Scientific, Singapore; Philadelphia, U.S.A., 1986).
115 Oohara, K., Nakamura, T., and Kojima, Y., “Apparent Horizons of Time-Symmetric Initial Value for Three Black Holes”, Phys. Lett. A, 107, 452–455, (1985).
116 Osher, S., and Sethian, J.A., “Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations”, J. Comput. Phys., 79, 12–49, (1988).
117 Parashar, M., and Browne, J.C., “System Engineering for High Performance Computing Software: The HDDA/DAGH Infrastructure for Implementation of Parallel Structured Adaptive Mesh Refinement”, in Baden, S.B., Chrisochoides, N.P., Gannon, D.B., and Norman, M.L., eds., Structured Adaptive Mesh Refinement (SAMR) Grid Methods, vol. 117 of IMA Volumes in Mathematics and its Applications, 1–18, (Springer, New York, U.S.A., 2000).
118 Pasch, E., The level set method for the mean curvature flow on (R3,g), SFB 382 Reports, 63, (University of Tübingen, Tübingen, Germany, 1997). URL (cited on 09 January 2006):
External Linkhttp://www.uni-tuebingen.de/uni/opx/reports.html.
119 Petrich, L.I., Shapiro, S.L., and Teukolsky, S.A., “Oppenheimer–Snyder Collapse with Maximal Time Slicing and Isotropic Coordinates”, Phys. Rev. D, 31, 2459–2469, (1985).
120 Pfeiffer, H.P., Initial Data for Black Hole Evolutions, Ph.D. Thesis, (Cornell University, Ithaca, U.S.A., 2003). Related online version (cited on 1 October 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0510016.
121 Pfeiffer, H.P., personal communication, (2006).
122 Pfeiffer, H.P., Cook, G.B., and Teukolsky, S.A., “Comparing initial-data sets for binary black holes”, Phys. Rev. D, 66, 024047, 1–17, (2002). Related online version (cited on 1 October 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0203085.
123 Pfeiffer, H.P., Kidder, L.E., Scheel, M.A., and Teukolsky, S.A., “A multidomain spectral method for solving elliptic equations”, Computer Phys. Commun., 152, 253–273, (2003). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0202096.
124 Pfeiffer, H.P., Teukolsky, S.A., and Cook, G.B., “Quasicircular orbits for spinning binary black holes”, Phys. Rev. D, 62, 104018, 1–11, (2000). Related online version (cited on 1 October 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0006084.
125 Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T., Numerical Recipes, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1992), 2nd edition.
126 Pretorius, F., and Choptuik, M.W., “Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems”, J. Comput. Phys., 218, 246–274, (2006). Related online version (cited on 3 October 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0508110.
127 Pretorius, F., and Lehner, L., “Adaptive mesh refinement for characteristic codes”, J. Comput. Phys., 198, 10–34, (2004). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0302003.
128 Regge, T., “General Relativity without Coordinates”, Nuovo Cimento A, 19, 558–571, (1961).
129 Richtmyer, R.D., and Morton, K.W., Difference Methods for Initial-Value Problems, (Krieger, Malabar, U.S.A., 1994), 2nd edition. Reprinted second edition of 1967.
130 Saad, Y., Iterative Methods for Sparse Linear Systems, (SIAM, Philadelphia, U.S.A., 2003), 2nd edition.
131 Schnetter, E., “CarpetCode: A mesh refinement driver for Cactus”, project homepage, Center for Computation and Technology, Louisiana State University. URL (cited on 09 January 2006):
External Linkhttp://www.carpetcode.org.
132 Schnetter, E., “A fast apparent horizon algorithm”, (2002). URL (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0206003.
133 Schnetter, E., “Finding Apparent Horizons and other Two-Surfaces of Constant Expansion”, Class. Quantum Grav., 20, 4719–4737, (2003). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0306006.
134 Schnetter, E., Hawley, S.H., and Hawke, I., “Evolutions in 3D numerical relativity using fixed mesh refinement”, Class. Quantum Grav., 21, 1465–1488, (2004). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0310042.
135 Schnetter, E., Herrmann, F., and Pollney, D., “Horizon Pretracking”, Phys. Rev. D, 71, 044033, (2005). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0410081.
136 Schnetter, E., and Krishnan, B., “Nonsymmetric trapped surfaces in the Schwarzschild Vaidya spacetimes”, Phys. Rev. D, 73, 021502, (2006). Related online version (cited on 3 October 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0511017.
137 Schnetter, E., Krishnan, B., and Beyer, F., “Introduction to Dynamical Horizons in numerical relativity”, Phys. Rev. D, 74, 024028, (2006). Related online version (cited on 30 October 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0604015.
138 Schroeder, M.R., Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing and Self-Similarity, vol. 7 of Springer Series in Information Sciences, (Springer, Berlin, Germany; New York, U.S.A., 1986), 2nd edition.
139 Seidel, E., and Suen, W.-M., “Towards a Singularity-Proof Scheme in Numerical Relativity”, Phys. Rev. Lett., 69, 1845–1848, (1992).
140 Shampine, L.F., and Gordon, M.K., Computer solution of Ordinary Differential Equations, (W.H. Freeman, San Francisco, U.S.A., 1975).
141 Shapiro, S.L., and Teukolsky, S.A., “Gravitational Collapse of Supermassive Stars to Black Holes: Numerical Solution of the Einstein Equations”, Astrophys. J. Lett., 234, L177–L181, (1979).
142 Shapiro, S.L., and Teukolsky, S.A., “Gravitational Collapse to Neutron Stars and Black Holes: Computer Generation of Spherical Spacetimes”, Astrophys. J., 235, 199–215, (1980). Related online version (cited on 05 February 2007):
External Linkhttp://adsabs.harvard.edu/abs/1980ApJ...235..199S.
143 Shapiro, S.L., and Teukolsky, S.A., “Relativistic stellar dynamics on the computer. I. Motivation and Numerical Method”, Astrophys. J., 298, 34–57, (1985).
144 Shapiro, S.L., and Teukolsky, S.A., “Relativistic stellar dynamics on the computer. II. Physical applications”, Astrophys. J., 298, 58–79, (1985).
145 Shapiro, S.L., and Teukolsky, S.A., “Collision of relativistic clusters and the formation of black holes”, Phys. Rev. D, 45, 2739–2750, (1992).
146 Shibata, M., “Apparent horizon finder for a special family of spacetimes in 3D numerical relativity”, Phys. Rev. D, 55, 2002–2013, (1997).
147 Shibata, M., and Uryū, K., “Apparent Horizon Finder for General Three-Dimensional Spaces”, Phys. Rev. D, 62, 087501, (2000).
148 Shoemaker, D.M., Apparent Horizons in Binary Black Hole Spacetimes, Ph.D. Thesis, (The University of Texas at Austin, Austin, U.S.A., 1999).
149 Shoemaker, D.M., Huq, M.F., and Matzner, R.A., “Generic tracking of multiple apparent horizons with level flow”, Phys. Rev. D, 62, 124005, (2000). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0006042.
150 Stoer, J., and Bulirsch, R., Introduction to Numerical Analysis, (Springer, Berlin, Germany; New York, U.S.A., 1980).
151 Szilágyi, B., Pollney, D., Rezzolla, L., Thornburg, J., and Winicour, J., “An explicit harmonic code for black-hole evolution using excision”, (2007). URL (cited on 09 April 2007):
External Linkhttp://arXiv.org/abs/gr-qc/0612150.
152 Teukolsky, S.A., “On the Stability of the Iterated Crank–Nicholson Method in Numerical Relativity”, Phys. Rev. D, 61, 087501, (2000).
153 Thornburg, J., “Finding apparent horizons in numerical relativity”, Phys. Rev. D, 54, 4899–4918, (1996). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9508014.
154 Thornburg, J., “A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes – I: Initial Data”, Phys. Rev. D, 59, 104007, (1999). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9801087.
155 Thornburg, J., “A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes – II: Time Evolution”, (1999). URL (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/9906022.
156 Thornburg, J., “A fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity”, Class. Quantum Grav., 21, 743–766, (2004). Related online version (cited on 09 January 2006):
External Linkhttp://arXiv.org/abs/gr-qc/0306056.
157 Tod, K.P., “Looking for marginally trapped surfaces”, Class. Quantum Grav., 8, L115–L118, (1991).
158 Trottenberg, U., Oosterlee, C.W., and Schüller, A., Multigrid, (Academic Press, San Diego, U.S.A., 2001).
159 Čadež, A., “Apparent Horizons in the Two-Black-Hole Problem”, Ann. Phys. (N.Y.), 83, 449–457, (1974).
160 Wald, R.M., General Relativity, (University of Chicago Press, Chicago, U.S.A., 1984).
161 Wald, R.M., and Iyer, V., “Trapped surfaces in the Schwarzschild geometry and cosmic censorship”, Phys. Rev. D, 44, R3719–R3722, (1991).
162 Walker, P., Horizons, Hyperbolic Systems, and Inner Boundary Conditions in Numerical Relativity, Ph.D. Thesis, (University of Illinois at Urbana-Champaign, Urbana, U.S.A., 1998).
163 York Jr, J.W., “Kinematics and Dynamics of General Relativity”, in Smarr, L.L., ed., Sources of Gravitational Radiation, Proceedings of the Battelle Seattle Workshop, July 24 – August 4, 1978, 83–126, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1979).
164 York Jr, J.W., “Initial Data for Collisions of Black Holes and Other Gravitational Miscellany”, in Evans, C.R., Finn, L.S., and Hobill, D.W., eds., Frontiers in Numerical Relativity, Proceedings of the International Workshop on Numerical Relativity, University of Illinois at Urbana-Champaign, U.S.A., May 9 – 13, 1988, 89–109, (Cambridge University Press, Cambridge, U.K.; New York, U.S.A., 1989).