Recent advances of strong-strong beam-beam simulation

In this paper, we report on recent advances in strong-strong beam-beam simulation. Numerical methods used in the calculation of the beam-beam forces are reviewed. A new computational method to solve the Poisson equation on nonuniform grid is presented. This method reduces the computational cost by a half compared with the standard FFT based method on uniform grid. It also appears to be more accurate than the standard method for a colliding beam with low transverse aspect ratio. In applications, we present the study of coherent modes with multi-bunch, multi-collision beam-beam interactions at RHIC. We also present the strong-strong simulation of the luminosity evolution at KEKB with and without finite crossing angle.