Towards standard testbeds for numerical relativity

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.

Numerical stability of the Alekseenko-Arnold evolution system compared to the ADM and BSSN systems

“…Since one aspect of the test suite put forward in [21] is that different numerical implementations of one and the same evolution system can be compared, let us point out that our results for ADM and BSSN agree with [21] for the specific results shown there (see also [31]). …”

“…Hence our initial data differ slightly form the ones in [21], who add random noise to all quantities which need initialization.…”

“…In Sec. III, we perform three tests from the recently proposed test suite [21] for numerical evolutions, the robust stability test, the gauge stability test, and the linear wave stability test. Finally, we evolve a single black hole space time in Sec.…”

Wave zone extraction of gravitational radiation in three-dimensional numerical relativity

“…We also hope that these results and these well-defined test cases can serve as a basis for future code validations and comparisons much in the spirit of Ref. [12].…”

General relativistic null-cone evolutions with a high-order scheme

“…A strong test for stability involves injecting (pseudo) random noise into the evolution, via the initial and boundary data [35,36]. By this method, any exponentially growing error modes, if present, will be stimulated at a much higher amplitude than would naturally occur due to truncation or round-off error.…”