PARALLELIZABLE IMPLICIT EVOLUTION SCHEME FOR REGGE CALCULUS

The role of Regge calculus as a tool for numerical relativity is discu ssed, and a parallelizable implicit evolution scheme described. Becaus e of the structure of the Regge equations, it is possible to advance t he vertices of a triangulated spacelike hypersurface in isolation, sol ving at each vertex a purely local system of implicit equations for th e new edge lengths involved. (In particular, equations of global ''ell iptic type'' do not arise.) Consequently, there exists a parallel evol ution scheme which divides the vertices into families of nonadjacent e lements and advances all the vertices of a family simultaneously. The relation between the structure of the equations of motion and the Bian chi identities is also considered. The method is illustrated by a prel iminary application to a 600-cell Friedmann cosmology. The paralleliza ble evolution algorithm described in this paper should enable Regge ca lculus to be a viable discretization technique in numerical relativity .