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| ⚫ | The goal of numerical relativity is to study ]s that cannot be studied by analytic means. The focus is therefore primarily on ]s. Numerical relativity has been applied in many areas: ] ], ], ] ]s and ]s, and the ]s and neutron stars, for example. In any of these cases, Einstein's equations can be formulated in several ways that allow us to evolve the dynamics. While ] methods have received a majority of the attention, characteristic and ] based methods have also been used. All of these methods begin with a snapshot of the ]s on some ], the initial data, and evolve these data to neighboring hypersurfaces. | ||
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| Despite promising results, accurate and validated ] for Einstein's equations remain elusive. The size and complexity of the equations along with persisting inquiries in fundamental issues of relativity theory are attributed the cause of thus far unsuccessful attempts at resolution. Nonetheless, the field has prodigiously expanded in recent years as engaging research continues. | |||
| Numerical relativity attempts to acquire a comprehensive understanding of the complex nature of strong dynamical gravitational fields. Another topic under investigation in numerical relativity is the ]. This involves ], discretization techniques for these equations, treatment of ] spacetimes, and the imposition of ]s. | |||
| Numerical relativity research is distinct from work on ] as many techniques implemented in these areas are inapplicable in relativity. Many facets are however shared with large scale problems in other computational sciences like ], electromagnetics, and solid mechanics. Numerical relativists often work with applied mathematicians and draw insight from ], ], ]s, and ] among other mathematical areas of specialization. | |||
| ==Computational aspects== | |||
| For D spatial dimensions in a simulation of, for example, a ] ] where physical phenomena are reduced to a set of difference equations (restricted to ]s) with a corresponding two dimensional NxN array of ]s and a ] of h, the ] time has ] O(''N''<sup>D+1</sup>) and the ] required has order O(''N''<sup>D</sup>). Coupled, non-linear, elliptic systems have O(N) computational work, where N is the number of discrete unknowns. | |||
| ==See also== | ==See also== | ||
Revision as of 05:28, 12 January 2006
The goal of numerical relativity is to study spacetimes that cannot be studied by analytic means. The focus is therefore primarily on dynamical systems. Numerical relativity has been applied in many areas: cosmological models, critical phenomena, perturbed black holes and neutron stars, and the coalescence of black holes and neutron stars, for example. In any of these cases, Einstein's equations can be formulated in several ways that allow us to evolve the dynamics. While Cauchy methods have received a majority of the attention, characteristic and Reggi calculus based methods have also been used. All of these methods begin with a snapshot of the gravitational fields on some hypersurface, the initial data, and evolve these data to neighboring hypersurfaces.
See also
Links
http://www.emis.ams.org/journals/LRG/Articles/lrr-2003-3/node19.html
http://xxx.lanl.gov/abs/gr-qc/9808024
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