ABSTRACT
The strong-strong beam-beam effect is one of the most important effects limiting the luminosity of ring colliders. Little is known about it analytically. so most studies utilize numeric simulations. The two-dimensional realm is readily accessible to workstation-class computers (cf.,e.g.,[ I, 2[). while three dimensions. which add effects such as phase averaging and the hourglass effect, require vastly higher amounts of CPU time. Thus, parallelization of three-dimensional simulation techniques is required: in the following, we consider several approaches, emphasizing computational aspects such as scalability. While the correctness of the code has been checked for analytically accessible cases, physical benchmarking and comparison with experimental results will be subject of a forthcoming paper.
