1994/11/03 by John W. Barrett, Mark Galassi, M. Galassi +4 · 55 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Algebra over a field #Applied mathematics #Black Holes and Theoretical Physics #Calculus (dental) #Cosmology and Gravitation Theories #Geometry #Mathematical analysis #Mathematics #Parallelizable manifold #Physics #Pure mathematics #Scheme (mathematics) #Theoretical physics #gr-qc
paper · pdf · doi:10.1007/bf02435787
published in International Journal of Theoretical Physics 36(4), 815-839 (Springer Science+Business Media) · 19 pages, Plain TeX, 10 figures
arxiv created 1994/11/03 · openalex publication_date 1997/04/01 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.