论文标题
在分层介质中的3-D线性泊松托架方程的快速多极方法
Fast Multipole Method for 3-D Linearized Poisson-Boltzmann Equation in Layered Media
论文作者
论文摘要
在本文中，我们为在分层介质中的3-D线性化泊松托架（PB）方程提出了一种快速多极方法（FMM）。该算法的主要框架使用Funk-Hecke公式的扩展，用于分层介质中的Helmholtz和Laplace方程[1,2]。此外，为FMM算法中使用的Sommerfeld型积分的运行时间计算提供了复发公式。由于Helmholtz和线性化的PB方程之间的相似性，因此在分层介质中，复发公式也可以用于helmholtz方程的FMM，如[1]中提到的较小的变化。数值结果验证了在分层介质中屏幕电势下电荷相互作用的FMM具有与自由空间中电荷相互作用的经典FMM相同的精度和CPU复杂性。
In this paper, we propose a fast multipole method (FMM) for 3-D linearized Poisson-Boltzmann (PB) equation in layered media. The main framework of the algorithm is analogous to the FMM for Helmholtz and Laplace equation in layered media [1,2], using an extension of the Funk-Hecke formula for pure imaginary wave number. Moreover, a recurrence formula is provided for the run-time computation of the Sommerfeld-type integrals used in the FMM algorithm. Due to the similarity between Helmholtz and linearized PB equation, the recurrence formula can also be used for the FMM of Helmholtz equation in layered media with minor changes as mentioned in [1] . Numerical results validate that the FMM for interactions of charges under screen's potentials in layered media has the same accuracy and CPU complexity as the classic FMM for charge interactions in free space.
