A Parallelizable Implicit Evolution Scheme for Regge Calculus
Abstract
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.
Cite
@article{arxiv.gr-qc/9411008,
title = {A Parallelizable Implicit Evolution Scheme for Regge Calculus},
author = {John W. Barrett and Mark Galassi and Warner A. Miller and Rafael D. Sorkin and Philip A. Tuckey and Ruth M. Williams},
journal= {arXiv preprint arXiv:gr-qc/9411008},
year = {2010}
}
Comments
19 pages, Plain TeX, 10 figures