A numerical study of the Regge Calculus and Smooth Lattice methods on a Kasner cosmology

TL;DR

This paper compares the accuracy and computational efficiency of Regge Calculus and Smooth Lattice Relativity methods in simulating Kasner cosmology, demonstrating convergence and significant speed differences.

Contribution

It provides the first detailed comparison of these two lattice-based numerical relativity methods on a Kasner cosmology, highlighting their convergence and performance.

Findings

Both methods produce convergent approximations.

Regge Calculus is approximately 110 times slower than Smooth Lattice.

Both methods accurately model Kasner cosmology.

Abstract

Two lattice based methods for numerical relativity, the Regge Calculus and the Smooth Lattice Relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge Calculus is of the order of 110 times slower than the Smooth Lattice method.