  The fast multipole method (FMM) has received growing attention in the beam
physics simulation. In this study, we formulate an interpolation-based FMM for
the computation of the relativistic space-charge field. Different to the
quasi-electrostatic model, our FMM is formulated in the lab-frame and can be
applied without the assistance of the Lorentz transformation. In particular, we
derive a modified admissibility condition which can effectively control the
interpolation error of the proposed FMM. The algorithms and their GPU
parallelization are discussed in detail. A package containing serial and
GPU-parallelized solvers is implemented in the Julia programming language. The
GPU-parallelized solver can reach a speedup of more than a hundred compared to
the execution on a single CPU core.
