Xue Changfeng, Deng Shaozhong
Department of Fundamental Sciences, Yancheng Institute of Technology, Yancheng, Jiangsu 224003, PR China.
Comput Phys Commun. 2008 Feb 1;178(3):171-185. doi: 10.1016/j.cpc.2007.08.015.
A recent article by Deng and Cai (Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: High-order image approximations for reaction fields, to appear in J. Comput. Phys.) introduced two fourth-order image approximations to the reaction field for a charge inside a dielectric sphere immersed in a solvent of low ionic strength. To represent such a reaction field, the image approximations employ a point charge at the classical Kelvin image point and two line charges that extend from this Kelvin image point along the radial direction to infinity, with one decaying to zero and the other growing to infinity. In this paper, alternative versions of the fourth-order image approximations are presented, using the same point charge but three different line charges, all decaying to zero along the radial direction. Similar discussions on how to approximate the line charges by discrete image charges and how to apply the resulting multiple discrete image approximations together with the fast multipole method are also included.
邓和蔡最近发表的一篇文章（《扩展用于离子溶剂中介电球内电荷的快速多极子方法：反应场的高阶镜像近似》，即将发表于《计算物理杂志》）介绍了两种针对低离子强度溶剂中浸没电介质球内电荷反应场的四阶镜像近似。为表示这样的反应场，镜像近似在经典开尔文镜像点处采用一个点电荷，并使用两条从该开尔文镜像点沿径向延伸至无穷远的线电荷，其中一条衰减至零，另一条增长至无穷大。在本文中，给出了四阶镜像近似的替代版本，使用相同的点电荷，但采用三条不同的线电荷，它们均沿径向衰减至零。文中还包含了关于如何用离散镜像电荷近似线电荷以及如何将所得的多个离散镜像近似与快速多极子方法一起应用的类似讨论。
