Toward standard testbeds for numerical relativity

TL;DR

This paper advocates for standardized testbeds in numerical relativity to systematically compare different evolution schemes, aiming to identify strengths, weaknesses, and sources of discrepancies in simulations of Einstein's equations.

Contribution

It introduces the concept and initial design of standardized testbeds for numerical relativity, facilitating fair comparison and analysis of various approaches.

Findings

Initial simple tests demonstrate effectiveness in revealing approach limitations.

Testbeds can distinguish differences caused by formulations, gauges, and boundary conditions.

Designed to be accessible and applicable to various numerical relativity methods.

Abstract

In recent years, many different numerical evolution schemes for Einstein's equations have been proposed to address stability and accuracy problems that have plagued the numerical relativity community for decades. Some of these approaches have been tested on different spacetimes, and conclusions have been drawn based on these tests. However, differences in results originate from many sources, including not only formulations of the equations, but also gauges, boundary conditions, numerical methods, and so on. We propose to build up a suite of standardized testbeds for comparing approaches to the numerical evolution of Einstein's equations that are designed to both probe their strengths and weaknesses and to separate out different effects, and their causes, seen in the results. We discuss general design principles of suitable testbeds, and we present an initial round of simple tests with periodic boundary conditions. This is a pivotal first step toward building a suite of testbeds to serve the numerical relativists and researchers from related fields who wish to assess the capabilities of numerical relativity codes. We present some examples of how these tests can be quite effective in revealing various limitations of different approaches, and illustrating their differences. The tests are presently limited to vacuum spacetimes, can be run on modest computational resources, and can be used with many different approaches used in the relativity community.