A Scheme to Numerically Evolve Data for the Conformal Einstein Equation

TL;DR

This paper details a numerical scheme for evolving data in the conformal Einstein equations, emphasizing the efficiency gains of a fourth order discretisation over second order methods.

Contribution

It introduces a numerical implementation that constructs complete data sets from minimal data and compares second and fourth order schemes for efficiency.

Findings

Fourth order scheme reduces memory and computation time by at least two orders of magnitude.

Complete data sets can be constructed from minimal data using the described numerical methods.

The paper provides technical details for implementing the numerical evolution of the conformal Einstein equations.

Abstract

This is the second paper in a series describing a numerical implementation of the conformal Einstein equation. This paper deals with the technical details of the numerical code used to perform numerical time evolutions from a "minimal" set of data. We outline the numerical construction of a complete set of data for our equations from a minimal set of data. The second and the fourth order discretisations, which are used for the construction of the complete data set and for the numerical integration of the time evolution equations, are described and their efficiencies are compared. By using the fourth order scheme we reduce our computer resource requirements --- with respect to memory as well as computation time --- by at least two orders of magnitude as compared to the second order scheme.