Lawrence Berkeley National Laboratory

In this paper, we report on recent advances in terascale simulations of the beam-beam interaction in Tevatron, RHIC and LHC. Computational methods for selfconsistent calculation of beam-beam forces are reviewed. New method for solving the two-dimensional Poisson equation with open boundary conditions is proposed and tested. This new spectral-finite difference method is a factor of four faster than the widely used FFT based Green function method for beam-beam interaction on axis. We also present applications to the study of antiproton losses during the injection stage at Tevatron, to the study of multiple bunch coherent beam-beam modes at RHIC, and to the study of beam-beam driven emittance growth at LHC.