A unique approach to numerical cosmology (and numerical
relativity in general) is the method of Regge Calculus in which
spacetime is represented as a complex of 4dimensional,
geometrically flat simplices. The principles of Einstein's theory
are applied directly to the simplicial geometry to form the
curvature, action and field equations, in contrast to the finite
difference approach where the continuum field equations are
differenced on a discrete mesh. A 3dimensional code implementing
Regge Calculus techniques was developed recently by Gentle and
Miller [32] 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 4dimensional regions or
lattices are used. The new method is analogous to York's
procedure [63] where the conformal metric, trace of the extrinsic curvature,
and momentum variables are all freely specifiable.
Although additional work is needed to apply (and develop)
Regge Calculus techniques to more general spacetimes, the early
results of Gentle and Miller are promising. In particular, their
evolutions have reproduced the continuum Kasner solution,
achieved second order convergence, and sustained numerical
stability.

Physical and Relativistic Numerical Cosmology
Peter Anninos
http://www.livingreviews.org/lrr19982
© MaxPlanckGesellschaft. ISSN 14338351
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