A DIRECT COMPARISON OF 2 CODES IN NUMERICAL RELATIVITY

We discuss a detailed numerical comparison of the results of two codes which treat the same model problem in numerical relativity. The model consists of a single, massless scalar field minimally coupled to the gravitational field with a further restriction to spherical symmetry. The comparison was complicated by the fact that the codes were based on different formalisms, used different coordinate systems and employed different numerical solution techniques. After briefly reviewing the model and our basic solution methods we describe in detail the additional numerical analysis which enabled us to directly (event-by-event) compare our solutions. We also describe some new algorithms which use Richardson extrapolation to significantly increase the accuracy of one of the codes at a given resolution. Using the basic methodology of convergence testing, and with the aid of high-accuracy (better than 0.001%) numerical results (also generated using extrapolation techniques), we find clear evidence that both codes are convergent even in the regime where the field interactions are significantly non-linear and highly time-dependent. We suggest that techniques such as those described in this paper will be very useful for testing codes which solve more general problems in numerical relativity.