论文标题
在强磁场下的一些电荷粒子动力学的某些分裂方案的错误估计值
Error estimates of some splitting schemes for charged-particle dynamics under strong magnetic field
论文作者
论文摘要
在这项工作中，我们考虑了强磁场下带电粒子动力学的某些分裂方案的误差估计。我们首先提出了一种新颖的节能拆分方案，每步的计算成本独立于磁场的强度。然后，在最大排序缩放情况下，我们为该方案建立了一类的Lie-Trotter类型分裂方案，均匀（以磁场的强度）以及在位置和磁场平行的速度中结合的最佳误差。对于一般的强磁场情况，构建了精确的调制傅立叶膨胀，并构建了数值溶液以获得收敛结果。提出了数值实验，以说明分裂方案的误差和能量行为。
In this work, we consider the error estimates of some splitting schemes for the charged-particle dynamics under a strong magnetic field. We first propose a novel energy-preserving splitting scheme with computational cost per step independent from the strength of the magnetic field. Then under the maximal ordering scaling case, we establish for the scheme and in fact for a class of Lie-Trotter type splitting schemes, a uniform (in the strength of the magnetic field) and optimal error bound in the position and in the velocity parallel to the magnetic field. For the general strong magnetic field case, the modulated Fourier expansions of the exact and the numerical solutions are constructed to obtain a convergence result. Numerical experiments are presented to illustrate the error and energy behaviour of the splitting schemes.
