Xiang Ming, Deng Shaozhong, Cai Wei
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA.
J Sci Comput. 2009 Dec 1;41(3):411-435. doi: 10.1007/s10915-009-9307-z.
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.
邓和蔡最近的一篇文章介绍了一种针对浸没在低离子强度溶剂中的电介质球内电荷的反应场的四阶图像近似。为了表示这样的反应场，图像近似在经典开尔文像点处采用一个点电荷，并使用从开尔文像点沿径向延伸至无穷远的两条线电荷。在本文中，利用相同的点电荷和三条不同的线电荷，开发了一种六阶图像近似。文中包含了如何通过点像电荷离散线电荷以及如何以O(N)复杂度实现所得点像近似以进行势场和力场计算的步骤。数值结果证明了图像近似的六阶收敛速率以及点像近似快速实现的O(N)复杂度。
