Mathematics
Scientific paper
Jul 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cqgra..23.....g&link_type=abstract
Classical and Quantum Gravity, Volume 23, Issue 16, pp. (2006).
Mathematics
Scientific paper
Two meeetings gave rise to this special issue on numerical relativity: the workshop 'Numerical relativity' at the Banff International Research Station on 16 21 April 2005 and the conference 'New directions in numerical relativity' which was held at Southampton University on the 18 and 19 August 2005 as a satellite meeting of the Newton Institute Programme 'Global problems in mathematical relativity'. This edition contains contributions drawn from these two meetings.
Looking back, 2005 will be remembered as the year in which key advances were made on a number of fronts which allowed significant progress in the binary black hole merger problem: at the Banff meeting, Frans Pretorius announced the first multi-orbit simulations, using a generalization of harmonic coordinates in which Friedrich's gauge source functions have been promoted to dynamical variables.
Then, at the 'Numerical Relativity 2005' meeting held on 2 4 November 2005 at NASA Goddard, the NASA Goddard and Texas/Brownsville groups independently (in back-to-back talks!) announced multi-orbit simulations with waveforms using the Baumgarte Shapiro Shibata Nakamura 3+1 formulation with improved hyperbolic lapse and shift drivers, and representing the black holes as wormholes ('punctures') moving through the grid.
These highlights were made possible by previous progress. Particularly important is the implementation of adaptive mesh refinement in general relativity in two and three dimensions, which not only allows for improved accuracy, but reduces the amount of time taken by 3D simulations, thus allowing systematic testing and improvement of 3D codes.
In addition, the community is now much more aware of the importance of well-posedness of the continuum problem and the stability of the numerical methods, and some formal investigations of these matters have caused practical improvements. The same applies for the role of gauge choices and boundary conditions.
Beyond the binary black hole problem, more incremental but steady progress is being made in neutron star merger and collapse simulations. The general relativity side of the simulations is just coming under control, and groups are now implementing more realistic matter models and, in particular, magneto-hydrodynamics. Vacuum and matter simulations will remain closely related. The investigation of critical collapse continues in 1D and 2D and remains a challenge for 3D codes. Additionally, work continues towards incorporating more refined numerical techniques for improved accuracy, stability and robustness.
Some, but not all, of these developments are reflected in the papers collected in this issue. They were invited mainly from participants of the two meetings above and make up this special issue which is the first of several that Classical and Quantum Gravity will publish. It is clear that many significant results are to be expected in the near future and will be reflected in this series.
Gundlach Carsten
Lehner Luis
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