Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

TL;DR

This paper develops and tests boundary conditions for Einstein equations that better preserve constraints and reduce reflections, improving stability in numerical simulations.

Contribution

It introduces a new set of well-posed, constraint-preserving boundary conditions for a harmonic Einstein formulation, enhancing numerical stability and accuracy.

Findings

Boundary conditions are less reflective than standard methods.

They effectively preserve constraints during simulations.

Tests include stability, linear, and nonlinear wave scenarios.

Abstract

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions.