An integral equation approach to calculate electrostatic interactions in many-body dielectric systems

Lindgren, Eric B.; Stace, Anthony J.; Polack, Etienne; Maday, Yvon; Stamm, Benjamin; Besley, Elena

Abstract

In this article, a numerical method to compute the electrostatic interaction energy and forces between many dielectric particles is presented. The computational method is based on a Galerkin approximation of an integral equation formulation, which is sufficiently general, as it is able to treat systems embedded in a homogeneous dielectric medium containing an arbitrary number of spherical particles of arbitrary size, charge, dielectric constant and position in the three-dimensional space. The algorithmic complexity is linear scaling with respect to the number of particles for the computation of the energy which has been achieved through the use of a modified fast multipole method. The method scales with the third power of the degree of spherical harmonics used in the underlying expansions, for general three-dimensional particle configurations. Several simple numerical examples illustrate the capabilities of the model, and the influence of mutual polarization between particles in an electrostatic interaction is discussed.

Citation

Lindgren, E. B., Stace, A. J., Polack, E., Maday, Y., Stamm, B., & Besley, E. (2018). An integral equation approach to calculate electrostatic interactions in many-body dielectric systems. Journal of Computational Physics, 371, 712-731. https://doi.org/10.1016/j.jcp.2018.06.015

• Journal Article Type: Article
• Acceptance Date: Jun 4, 2018
• Online Publication Date: Jun 6, 2018
• Publication Date: 2018-10
• Deposit Date: Mar 26, 2020
• Journal: Journal of Computational Physics
• Print ISSN: 0021-9991
• Electronic ISSN: 1090-2716
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 371
• Pages: 712-731
• DOI: https://doi.org/10.1016/j.jcp.2018.06.015
• Keywords: Physics and Astronomy (miscellaneous); Computer Science Applications
• Public URL: https://nottingham-repository.worktribe.com/output/3018637
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0021999118303930
• Additional Information: This article is maintained by: Elsevier; Article Title: An integral equation approach to calculate electrostatic interactions in many-body dielectric systems; Journal Title: Journal of Computational Physics; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jcp.2018.06.015; Content Type: article; Copyright: Crown Copyright © 2018 Published by Elsevier Inc. All rights reserved.