A GPU-Parallelized Interpolation-Based Fast Multipole Method for the Relativistic Space-Charge Field Calculation

TL;DR

This paper introduces a GPU-accelerated interpolation-based fast multipole method for relativistic space-charge field calculations, operating directly in the lab frame without Lorentz transformations, and achieving significant speedups.

Contribution

It formulates a novel interpolation-based FMM for relativistic fields in the lab frame, with a modified admissibility condition and GPU parallelization, implemented in Julia.

Findings

GPU solver achieves over 100x speedup over CPU

Effective control of interpolation error with new admissibility condition

Applicable directly in the lab frame without Lorentz transformation

Abstract

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.