论文标题
在用于带电颗粒动力学的大型集成器上
On a large-stepsize integrator for charged-particle dynamics
论文作者
论文摘要
Xiao和QIN [计算机物理通讯，265：107981，2021]最近提出了对鲍里斯算法进行了非常简单的修改，以计算带电粒子高度振荡运动的指导中心，其台阶尺寸的尺寸比吉尔（Gyrorotations）时期大得多。他们提供了有力的数值证据，但没有错误分析。本文在具有强烈的不均匀磁场和中度界限的设置中，对大型修饰的鲍里斯方法进行了分析，该设置在固定有限的时间间隔内考虑。错误分析基于比较精确和数值解的调制傅立叶扩展，为此，明确得出了主要项的微分方程。数值实验说明并补充理论结果。
Xiao and Qin [Computer Physics Comm., 265:107981, 2021] recently proposed a remarkably simple modification of the Boris algorithm to compute the guiding centre of the highly oscillatory motion of a charged particle with step sizes that are much larger than the period of gyrorotations. They gave strong numerical evidence but no error analysis. This paper provides an analysis of the large-stepsize modified Boris method in a setting that has a strong non-uniform magnetic field and moderately bounded velocities, considered over a fixed finite time interval. The error analysis is based on comparing the modulated Fourier expansions of the exact and numerical solutions, for which the differential equations of the dominant terms are derived explicitly. Numerical experiments illustrate and complement the theoretical results.
