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A Parallelizable Implicit Evolution Scheme for Regge Calculus

John W. Barrett·Mark Galassi·Warner A. Miller·Rafael D. Sorkin·Philip A. Tuckey·Ruth M. Williams
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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.

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John W. Barrett, Mark Galassi, Warner A. Miller, Rafael D. Sorkin, Philip A. Tuckey, Ruth M. Williams. 1994-11-03. A Parallelizable Implicit Evolution Scheme for Regge Calculus. https://doi.org/10.1007/bf02435787

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