Constructing of constraint preserving scheme for Einstein equations

TL;DR

This paper introduces a new numerical scheme based on the discrete variational derivative method for evolving Einstein equations, which effectively preserves constraints and demonstrates improved numerical stability over traditional methods.

Contribution

The paper develops a novel constraint-preserving numerical scheme for Einstein equations using DVDM, enhancing stability and constraint preservation at the discrete level.

Findings

The new scheme preserves constraints in the discrete evolution.

Numerical simulations show improved stability over Crank-Nicolson.

The scheme is effective for stable evolution of Einstein equations.

Abstract

We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint preserves in the discrete level. In addition, to confirm the numerical stability using this scheme, we perform some numerical simulations by discretized equations with the Crank-Nicolson scheme and with the new scheme, and we find that the new discretized equations have better stability than that of the Crank-Nicolson scheme.