In this paper we present a new approach, based on a shifted Green function, to evaluate the electromagnetic field in a simulation of colliding beams. Unlike a conventional particle-mesh code, we use a method in which the computational mesh covers only the largest of the two colliding beams. This allows us to study long-range parasitic collisions accurately and efficiently. We have implemented this algorithm in a new parallel strong-strong beam-beam simulation code. As an application, we present a study of a beam sweeping scheme for the LBNL luminosity monitor of the Large Hadron Collider.
