论文标题
用于计算$ n $ body介电球问题的精确数值方法的线性缩放
A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem
论文作者
论文摘要
本文介绍了经历相互极化的带电的球形介电颗粒之间的静电力的有效计算。我们使用Lindgren等人开发的光谱Galerkin边界积分方程框架。 （J.Comput。Phys。371（2018）：712-731），随后对作者的两个早期贡献进行了分析，以提出成本算法的线性缩放，以计算近似力的计算。我们建立了该方法的指数收敛，并得出了不明确取决于介电粒子$ n $的近似力的误差估计。因此，所提出的方法仅需要$ \ MATHCAL {O}（N）$操作来计算作用于$ N $介电粒子的静电力，直到任何给定和固定的相对误差。
This article deals with the efficient and accurate computation of the electrostatic forces between charged, spherical dielectric particles undergoing mutual polarisation. We use the spectral Galerkin boundary integral equation framework developed by Lindgren et al. (J. Comput. Phys. 371 (2018): 712-731) and subsequently analysed in two earlier contributions of the authors to propose a linear scaling in cost algorithm for the computation of the approximate forces. We establish exponential convergence of the method and derive error estimates for the approximate forces that do not explicitly depend on the number of dielectric particles $N$. Consequently, the proposed method requires only $\mathcal{O}(N)$ operations to compute the electrostatic forces acting on $N$ dielectric particles up to any given and fixed relative error.
