Rigorous simulation, which in concept is nearly linear in CPU time with microampere beam currents, has been developed for analyzing statistical electron-electron interactions in lens free regions joined by ideal lenses and apertures. The simulation method is based on combining fast multipole acceleration (FMA) with modifications to a message passing interface for use on a multiprocessor and on a network of workstations. As test cases, the distribution of scattered electrons versus deviation from focus is given as well as results for the interaction between simultaneously imaged spots. The performance improvement per level of spatial division was only about a factor of 2 instead of the expected factor of 8 due to the pencil shape nature of the beam. A FMA method that is adaptable to beam density and geometry is needed. It is projected that it will be possible to simulate a 30 mu A beam current on a quad-Pentium Pro machine in half a day and in matter of hour on a network of workstations.