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

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

Author Details

Muhammad Hassan

Benjamin Stamm

  1. The significance of multipole interactions for the stability of regular structures composed from charged particles

    Lindgren, Eric B. | Avis, Holly | Miller, Abigail | Stamm, Benjamin | Besley, Elena | Stace, Anthony J.

    Journal of Colloid and Interface Science, Vol. 663 (2024), Iss. P.458

    https://doi.org/10.1016/j.jcis.2024.02.146 [Citations: 1]

  2. Manipulating Interactions between Dielectric Particles with Electric Fields: A General Electrostatic Many-Body Framework

    Hassan, Muhammad | Williamson, Connor | Baptiste, Joshua | Braun, Stefanie | Stace, Anthony J. | Besley, Elena | Stamm, Benjamin

    Journal of Chemical Theory and Computation, Vol. 18 (2022), Iss. 10 P.6281

    https://doi.org/10.1021/acs.jctc.2c00008 [Citations: 2]