A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem

Communications in Computational Physics, vol. 29, pp. 319–356

Abstract

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.

Authors 2

1. Muhammad Hassan Aachen Center for Computational Engineering Science Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany

   Center for Computational Engineering Science, Department of Mathematics, RWTH Aachen University, Schinkelstrasse 2, 52062 Aachen, Germany

2. Benjamin Stamm Aachen Center for Computational Engineering Science Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany

   Center for Computational Engineering Science, Department of Mathematics, RWTH Aachen University, Schinkelstrasse 2, 52062 Aachen, Germany