A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem (Communications in Computational Physics, 2020)
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 developedby Lindgren et al. (J. Comput. Phys. 371 (2018): 712-731) and subsequently analysedin two earlier contributions of the authors to propose a linear scaling in cost algorithmfor the computation of the approximate forces. We establish exponential convergenceof the method and derive error estimates for the approximate forces that do not explicitly depend on the number of dielectric particles $N$. Consequently, the proposedmethod requires only $\mathcal{O}(N) $ operations to compute the electrostatic forces acting on $N$ dielectric particles up to any given and fixed relative error.