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.