A 3-dimensional code implementing Regge Calculus techniques was developed recently by Gentle and Miller  and applied to the Kasner cosmological model. They also describe a procedure to solve the constraint equations for time asymmetric initial data on two spacelike hypersurfaces constructed from tetrahedra, since full 4-dimensional regions or lattices are used. The new method is analogous to York's procedure (see  and § 6.4) where the conformal metric, trace of the extrinsic curvature, and momentum variables are all freely specifiable. These early results are promising in that they have reproduced the continuum Kasner solution, achieved second order convergence, and sustained numerical stability. Also, Barnett et al.  discuss an implicit evolution scheme that allows local (vertex) calculations for efficient parallelism. However, the Regge Calculus approach remains to be developed and applied to more general spacetimes with complex topologies, extended degrees of freedom, and general source terms.
Computational Cosmology: from the Early Universe to the Large Scale Structure
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