A framework for large-scale relativistic simulations in the characteristic approach

TL;DR

This paper introduces LEO, a new computational framework enabling large-scale, high-resolution simulations in numerical relativity using the characteristic approach, with demonstrated scalability and accuracy in scalar field and gravitational problems.

Contribution

The paper presents a novel, highly parallel numerical code based on an improved eth formalism and a first-order reduction of Einstein equations for large-scale relativistic simulations.

Findings

Successfully simulated scalar fields coupled to gravity in 3D

Achieved second-order convergence and excellent scaling

Observed energy flow saturation at the Schwarzschild radius

Abstract

We present a new computational framework (LEO), that enables us to carry out the very first large-scale, high-resolution computations in the context of the characteristic approach in numerical relativity. At the analytic level, our approach is based on a new implementation of the ``eth'' formalism, using a non-standard representation of the spin-raising and lowering angular operators in terms of non-conformal coordinates on the sphere; we couple this formalism to a partially first-order reduction (in the angular variables) of the Einstein equations. The numerical implementation of our approach supplies the basic building blocks for a highly parallel, easily extensible numerical code. We demonstrate the adaptability and excellent scaling of our numerical code by solving, within our numerical framework, for a scalar field minimally coupled to gravity (the Einstein-Klein-Gordon problem) in 3-dimensions. The nonlinear code is globally second-order convergent, and has been extensively tested using as reference a calibrated code with the same boundary-initial data and radial marching algorithm. In this context, we show how accurately we can follow quasi-normal mode ringing. In the linear regime, we show energy conservation for a number of initial data sets with varying angular structure. A striking result that arises in this context is the saturation of the flow of energy through the Schwarzschild radius. As a final calibration check we perform a large simulation with resolution never achieved before.