GRChombo: numerical relativity with adaptive mesh refinement. (English) Zbl 1331.83003
Summary: In this work, we introduce GRChombo: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured Berger-Rigoutsos grid generation. The code supports non-trivial ‘many-boxes-in-many-boxes’ mesh hierarchies and massive parallelism through the message passing interface. GRChombo evolves the Einstein equation using the standard BSSN formalism, with an option to turn on CCZ4 constraint damping if required. The AMR capability permits the study of a range of new physics which has previously been computationally infeasible in a full 3+1 setting, while also significantly simplifying the process of setting up the mesh for these problems. We show that GRChombo can stably and accurately evolve standard spacetimes such as binary black hole mergers and scalar collapses into black holes, demonstrate the performance characteristics of our code, and discuss various physics problems which stand to benefit from the AMR technique.
MSC:
| 83-08 | Computational methods for problems pertaining to relativity and gravitational theory |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
References:
| [1] | Einstein A 1916 Die grundlage der allgemeinen relativitätstheorie Ann. Phys., Lpz.354 769–822 · JFM 46.1293.01 · doi:10.1002/andp.19163540702 |
| [2] | Pretorius F 2005 Evolution of binary black hole spacetimes Phys. Rev. Lett.95 121101 · doi:10.1103/PhysRevLett.95.121101 |
| [3] | Baker J G, Centrella J, Choi D-I, Koppitz M and van Meter J 2006 Gravitational wave extraction from an inspiraling configuration of merging black holes Phys. Rev. Lett.96 111102 · doi:10.1103/PhysRevLett.96.111102 |
| [4] | Campanelli M, Lousto C, Marronetti P and Zlochower Y 2006 Accurate evolutions of orbiting black-hole binaries without excision Phys. Rev. Lett.96 111101 · doi:10.1103/PhysRevLett.96.111101 |
| [5] | Berti E et al 2015 Testing general relativity with present and future astrophysical observations arXiv:1501.07274[gr-qc] |
| [6] | Wainwright C L, Johnson M C, Aguirre A and Peiris H V 2014 Simulating the Universe(s): II. Phenomenology of cosmic bubble collisions in full general relativity J. Cosmol. Astropart. Phys. JCAP10(2014)024 |
| [7] | Johnson M C, Peiris H V and Lehner L 2012 Determining the outcome of cosmic bubble collisions in full general relativity Phys. Rev. D 85 083516 · doi:10.1103/PhysRevD.85.083516 |
| [8] | Cardoso V et al 2012 NR/HEP: roadmap for the future Class. Quantum Grav.29 244001 |
| [9] | Chesler P M and Yaffe L G 2014 Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes J. High Energy Phys. JHEP07(2014)086 · Zbl 1421.81111 · doi:10.1007/JHEP07(2014)086 |
| [10] | Cardoso V, Gualtieri L, Herdeiro C and Sperhake U 2015 Exploring new physics frontiers through numerical relativity Living Reviews in Relativity18 1 · doi:10.1007/lrr-2015-1 |
| [11] | Choptuik M W, Lehner L and Pretorius F 2015 Probing strong field gravity through numerical simulations arXiv:1502.06853[gr-qc] |
| [12] | Goodale T, Allen G, Lanfermann G, Massó J, Radke T, Seidel E and Shalf J 2003 The cactus framework and toolkit: design and applications Vector and Parallel Processing–VECPAR2002, 5th Int. Conf., Lecture Notes in Computer Science (Berlin: Springer) · Zbl 1027.65524 · doi:10.1007/3-540-36569-9_13 |
| [13] | Loffler F et al 2012 The Einstein toolkit: a community computational infrastructure for relativistic astrophysics Class. Quantum Grav.29 115001 |
| [14] | Brown J D, Diener P, Sarbach O, Schnetter E and Tiglio M 2009 Turduckening black holes: an analytical and computational study Phys. Rev. D 79 044023 · doi:10.1103/PhysRevD.79.044023 |
| [15] | Kranc: Kranc Assembles Numerical Code. Online. http://kranccode.org/ |
| [16] | Baumgarte T W and Shapiro S L 1999 On the numerical integration of Einstein’s field equations Phys. Rev. D 59 024007 · Zbl 1250.83004 · doi:10.1103/PhysRevD.59.024007 |
| [17] | Shibata M and Nakamura T 1995 Evolution of three-dimensional gravitational waves: harmonic slicing case Phys. Rev. D 52 5428–44 · Zbl 1250.83027 · doi:10.1103/PhysRevD.52.5428 |
| [18] | Sperhake U 2007 Binary black-hole evolutions of excision and puncture data Phys. Rev. D 76 104015 · doi:10.1103/PhysRevD.76.104015 |
| [19] | Zilhao M, Witek H, Sperhake U, Cardoso V, Gualtieri L, Herdeiro C and Nerozzi A 2010 Numerical relativity for D dimensional axially symmetric space–times: formalism and code tests Phys. Rev. D 81 084052 · doi:10.1103/PhysRevD.81.084052 |
| [20] | Marronetti P, Tichy W, Bruegmann B, Gonzalez J, Hannam M, Husa S and Sperhake U 2007 Binary black holes on a budget: simulations using workstations Class. Quantum Grav.24 43–58 |
| [21] | Cao Z and Hilditch D 2012 Numerical stability of the Z4c formulation of general relativity Phys. Rev. D 85 124032 · doi:10.1103/PhysRevD.85.124032 |
| [22] | Galaviz P, Brügmann B and Cao Z 2010 Numerical evolution of multiple black holes with accurate initial data Phys. Rev. D 82 024005 · doi:10.1103/PhysRevD.82.024005 |
| [23] | The Einstein Toolkit. Online., http://einsteintoolkit.org/ |
| [24] | Pfeiffer H P, Kidder L E, Scheel M A and Teukolsky S A 2003 A multidomain spectral method for solving elliptic equations Comput. Phys. Commun.152 253–73 · Zbl 1196.65179 · doi:10.1016/S0010-4655(02)00847-0 |
| [25] | Hilditch D, Weyhausen A and Bruegmann B 2015 A pseudospectral method for gravitational wave collapse arXiv:1504.04732[gr-qc] |
| [26] | PAMR (Parallel Adaptive Mesh Refinement) and AMRD (Adaptive Mesh Refinement Driver) libraries., http://laplace.physics.ubc.ca/Group/Software.html |
| [27] | Neilsen D, Hirschmann E W, Anderson M and Liebling S L 2007 Adaptive mesh refinement and relativistic MHD Recent developments in theoretical and experimental general relativity, gravitation and relativistic field theories. Proc. 11th Marcel Grossmann Meeting, MG11(Berlin, Germany, 23–29 July 2006) pp 1579–1581 Pt. A-C |
| [28] | Adams M et al 2013 Chombo software package for amr applications–design document Technical Report LBNL-6616E Lawrence Berkeley National Laboratory |
| [29] | Alic D, Bona-Casas C, Bona C, Rezzolla L and Palenzuela C 2012 Conformal and covariant formulation of the Z4 system with constraint-violation damping Phys. Rev. D 85 064040 · doi:10.1103/PhysRevD.85.064040 |
| [30] | Bona C, Ledvinka T, Palenzuela C and Zacek M 2003 General covariant evolution formalism for numerical relativity Phys. Rev. D 67 104005 · doi:10.1103/PhysRevD.67.104005 |
| [31] | Berger M J and Rigoutsos I 1991 An algorithm for Point Clustering and Grid Generation IEEE Trans. Syst. Man. Cyber.21 1278–86 · doi:10.1109/21.120081 |
| [32] | Babiuc M et al 2008 Implementation of standard testbeds for numerical relativity Class. Quantum Grav.25 125012 · Zbl 1144.83002 |
| [33] | Nakamura T, Oohara K and Kojima Y 1987 General relativistic collapse to black holes and gravitational waves from black holes Prog. Theor. Phys. Suppl.90 1–218 · doi:10.1143/PTPS.90.1 |
| [34] | Bona C, Masso J, Seidel E and Stela J 1995 A new formalism for numerical relativity Phys. Rev. Lett.75 600–3 · doi:10.1103/PhysRevLett.75.600 |
| [35] | Alcubierre M et al 2003 Gauge conditions for long term numerical black hole evolutions without excision Phys. Rev. D 67 084023 · doi:10.1103/PhysRevD.67.084023 |
| [36] | Gundlach C, Martin-Garcia J M, Calabrese G and Hinder I 2005 Constraint damping in the Z4 formulation and harmonic gauge Class. Quantum Grav.22 3767–74 · Zbl 1154.83302 |
| [37] | Bernuzzi S and Hilditch D 2010 Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4 Phys. Rev. D 81 084003 · doi:10.1103/PhysRevD.81.084003 |
| [38] | Brown J D 2009 Covariant formulations of BSSN and the standard gauge Phys. Rev. D 79 104029 · doi:10.1103/PhysRevD.79.044023 |
| [39] | Baumgarte T W, Montero P J, Cordero-Carrion I and Muller E 2013 Numerical relativity in spherical polar coordinates: evolution calculations with the BSSN formulation Phys. Rev. D 87 044026 · doi:10.1103/PhysRevD.87.044026 |
| [40] | Sanchis-Gual N, Montero P J, Font J A, Müller F and Baumgarte T W 2014 Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry Phys. Rev. D 89 104033 · Zbl 1329.83052 · doi:10.1103/PhysRevD.89.104033 |
| [41] | Baumgarte T W and Shapiro S L 2010 Numerial Relativity : Solving Einstein’s Equations on the Computer (Cambridge: Cambridge University Press) · doi:10.1017/CBO9781139193344 |
| [42] | Alic D, Kastaun W and Rezzolla L 2013 Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars Phys. Rev. D 88 064049 · doi:10.1103/PhysRevD.88.064049 |
| [43] | Berger M and Oliger J 1984 Adaptive mesh refinement for hyperbolic partial differential equations J. Comput. Phys. 484–512 · Zbl 0536.65071 · doi:10.1016/0021-9991(84)90073-1 |
| [44] | Berger M J and Colella P 1989 Local adaptive mesh refinement for shock hydrodynamics J. Comput. Phys.82 64–84 · Zbl 0665.76070 · doi:10.1016/0021-9991(89)90035-1 |
| [45] | Zlochower Y, Baker J, Campanelli M and Lousto C 2005 Accurate black hole evolutions by fourth-order numerical relativity Phys. Rev. D 72 024021 · doi:10.1103/PhysRevD.72.024021 |
| [46] | Kreiss H-O and Oliger J 1972 Comparison of accurate methods for the integration of hyperbolic equations Tellus24 199–215 · doi:10.1111/j.2153-3490.1972.tb01547.x |
| [47] | Choptuik M W 1993 Universality and scaling in gravitational collapse of a massless scalar field Phys. Rev. Lett.70 9–12 · doi:10.1103/PhysRevLett.70.9 |
| [48] | Gundlach C and Martin-Garcia J M 2007 Critical phenomena in gravitational collapse Living Rev. Relativ.10 5 · Zbl 1175.83037 · doi:10.12942/lrr-2007-5 |
| [49] | Abrahams A and Evans C 1993 Critical behavior and scaling in vacuum axisymmetric gravitational collapse Phys. Rev. Lett.70 2980–3 · doi:10.1103/PhysRevLett.70.2980 |
| [50] | Choptuik M W, Hirschmann E W, Liebling S L and Pretorius F 2003 Critical collapse of the massless scalar field in axisymmetry Phys. Rev. D 68 044007 · Zbl 1244.83004 · doi:10.1103/PhysRevD.68.044007 |
| [51] | Sorkin E 2011 On critical collapse of gravitational waves Class. Quantum Grav.28 025011 · Zbl 1207.83041 |
| [52] | Healy J and Laguna P 2014 Critical collapse of scalar fields beyond axisymmetry Gen. Relativ. Gravit.46 1722 · Zbl 1291.83141 · doi:10.1007/s10714-014-1722-2 |
| [53] | Hilditch D, Baumgarte T W, Weyhausen A, Dietrich T, Brügmann B, Montero P J and Müller E 2013 Collapse of nonlinear gravitational waves in moving-puncture coordinates Phys. Rev. D 88 103009 · doi:10.1103/PhysRevD.88.103009 |
| [54] | Emparan R and Reall H S 2002 A Rotating black ring solution in five-dimensions Phys. Rev. Lett.88 101101 · doi:10.1103/PhysRevLett.88.101101 |
| [55] | Gregory R and Laflamme R 1993 Black strings and p-branes are unstable Phys. Rev. Lett.70 2837–40 · Zbl 1051.83544 · doi:10.1103/PhysRevLett.70.2837 |
| [56] | Emparan R and Myers R C 2003 Instability of ultra-spinning black holes J. High Energy Phys. JHEP09(2003)025 |
| [57] | Dias O J C, Figueras P, Monteiro R, Santos J E and Emparan R 2009 Instability and new phases of higher-dimensional rotating black holes Phys. Rev. D 80 111701 · doi:10.1103/PhysRevD.80.111701 |
| [58] | Dias O J C, Figueras P, Monteiro R, Reall H S and Santos J E 2010 An instability of higher-dimensional rotating black holes J. High Energy Phys. JHEP05(2010)076 · Zbl 1287.83031 · doi:10.1007/JHEP05(2010)076 |
| [59] | Shibata M and Yoshino H 2010 Bar-mode instability of rapidly spinning black hole in higher dimensions: numerical simulation in general relativity Phys. Rev. D 81 104035 · doi:10.1103/PhysRevD.81.104035 |
| [60] | Bizon P and Rostworowski A 2011 On weakly turbulent instability of anti-de Sitter space Phys. Rev. Lett.107 031102 · doi:10.1103/PhysRevLett.107.031102 |
| [61] | Maldacena J M 1999 The Large N limit of superconformal field theories and supergravity Int. J. Theor. Phys.38 1113–33 · Zbl 0969.81047 · doi:10.1023/A:1026654312961 |
| [62] | Maldacena J M 1998 Adv. Theor. Math. Phys.2 231 |
| [63] | Emparan R and Reall H S 2008 Black holes in higher dimensions Living Rev. Relativ.11 6 · Zbl 1166.83002 · doi:10.12942/lrr-2008-6 |
| [64] | Horowitz G T 2012 Black Holes in Higher Dimensions (Cambridge: Cambridge University Press) · Zbl 1241.83007 · doi:10.1017/CBO9781139004176 |
| [65] | Lehner L and Pretorius F 2010 Black strings, low viscosity fluids, and violation of cosmic censorship Phys. Rev. Lett.105 101102 · doi:10.1103/PhysRevLett.105.101102 |
| [66] | Holzegel G and Smulevici J 2013 Decay properties of Klein-Gordon fields on Kerr-AdS spacetimes Commun. Pure. Appl. Math.66 1751–802 · Zbl 1277.83023 · doi:10.1002/cpa.21470 |
| [67] | Carrasco F, Lehner L, Myers R C, Reula O and Singh A 2012 Turbulent flows for relativistic conformal fluids in 2 + 1 dimensions Phys. Rev. D 86 126006 · doi:10.1103/PhysRevD.86.126006 |
| [68] | Adams A, Chesler P M and Liu H 2014 Holographic turbulence Phys. Rev. Lett.112 151602 · doi:10.1103/PhysRevLett.112.151602 |
| [69] | Yang H, Zimmerman A and Lehner L 2015 Turbulent black holes Phys. Rev. Lett.114 081101 · doi:10.1103/PhysRevLett.114.081101 |
| [70] | Yoshino H and Shibata M 2009 Higher-dimensional numerical relativity: formulation and code tests Phys. Rev. D 80 084025 · doi:10.1103/PhysRevD.80.084025 |
| [71] | Bantilan H, Pretorius F and Gubser S S 2012 Simulation of asymptotically AdS5 spacetimes with a generalized harmonic evolution scheme Phys. Rev. D 85 084038 · doi:10.1103/PhysRevD.85.084038 |
| [72] | Alcubierre M 2008 Introduction to 3+1 Numerical Relativity (Oxford: Oxford University Press) · Zbl 1140.83002 · doi:10.1093/acprof:oso/9780199205677.001.0001 |
| [73] | Hannam M, Husa S, Ohme F, Bruegmann B and O’Murchadha N 2008 Wormholes and trumpets: the Schwarzschild spacetime for the moving-puncture generation Phys. Rev. D 78 064020 · doi:10.1103/PhysRevD.78.064020 |
| [74] | Brandt S R and Seidel E 1996 The Evolution of distorted rotating black holes: III. Initial data Phys. Rev. D 54 1403–16 · doi:10.1103/PhysRevD.54.1403 |
| [75] | Cactus Computational Toolkit., http://cactuscode.org/ |
| [76] | Schnetter E, Hawley S H and Hawke I 2004 Evolutions in 3-D numerical relativity using fixed mesh refinement Class. Quantum Grav.21 1465–88 · Zbl 1047.83002 |
| [77] | http://carpetcode.org/ Carpet: Adaptive Mesh Refinement for the Cactus Framework. |
| [78] | Ansorg M, Bruegmann B and Tichy W 2004 A Single-domain spectral method for black hole puncture data Phys. Rev. D 70 064011 · doi:10.1103/PhysRevD.70.064011 |
| [79] | Thornburg J 2004 A Fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity Class. Quantum Grav.21 743–66 · Zbl 1045.83006 |
| [80] | Thornburg J 1996 Finding apparent horizons in numerical relativity Phys. Rev. D 54 4899–918 · doi:10.1103/PhysRevD.54.4899 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
