A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the $N$-Body Dielectric Spheres Problem
Year: 2021
Author: Muhammad Hassan, Benjamin Stamm
Communications in Computational Physics, Vol. 29 (2021), Iss. 2 : 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2020-0090
Communications in Computational Physics, Vol. 29 (2021), Iss. 2 : pp. 319–356
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: Boundary integral equations error analysis $N$-body problem linear scaling polarisation forces.