  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.
