A recent article by Deng and Cai introduced 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 the Kelvin image point along the radial direction to infinity. In this paper, a sixth-order image approximation is developed, using the same point charge with three different line charges. Procedures on how to discretize the line charges by point image charges and how to implement the resulting point image approximation in O(N) complexity for potential and force field calculations are included. Numerical results demonstrate the sixth-order convergence rate of the image approximation and the O(N) complexity of the fast implementation of the point image approximation.

中文翻译：

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离子溶剂诱导反应场的六阶图像近似。

Deng 和 Cai 最近的一篇文章介绍了浸入低离子强度溶剂中的介电球内电荷反应场的四阶图像近似。为了表示这样的反应场，图像近似采用经典开尔文图像点处的点电荷和从开尔文图像点沿径向延伸到无穷远的两个线电荷。在本文中，使用具有三个不同线电荷的相同点电荷开发了六阶图像近似。包括如何通过点图像电荷离散线电荷以及如何在 O(N) 复杂度中实现所得点图像近似以进行势场和力场计算的程序。