Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1994-11-03
Int.J.Theor.Phys.36:815-840,1997
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, Plain TeX, 10 figures
Scientific paper
10.1007/BF02435787
The role of Regge calculus as a tool for numerical relativity is discussed, and a parallelizable implicit evolution scheme described. Because of the structure of the Regge equations, it is possible to advance the vertices of a triangulated spacelike hypersurface in isolation, solving at each vertex a purely local system of implicit equations for the new edge-lengths involved. (In particular, equations of global ``elliptic-type'' do not arise.) Consequently, there exists a parallel evolution scheme which divides the vertices into families of non-adjacent elements and advances all the vertices of a family simultaneously. The relation between the structure of the equations of motion and the Bianchi identities is also considered. The method is illustrated by a preliminary application to a 600--cell Friedmann cosmology. The parallelizable evolution algorithm described in this paper should enable Regge calculus to be a viable discretization technique in numerical relativity.
Barrett John W.
Galassi Mark
Miller Warner A.
Sorkin Rafael D.
Tuckey Philip A.
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