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.,(1, 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 imperative; in the following we discuss parallelization strategies and describe the algorithms used in our simulation code, which will reach almost linear scaling of performance vs. number of CPUs for typical setups.