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

• Published in: Journal of computational physics Vol. 371; pp. 712 - 731
• Main Authors: Lindgren, Eric B., Stace, Anthony J., Polack, Etienne, Maday, Yvon, Stamm, Benjamin, Besley, Elena
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 15.10.2018; Elsevier Science Ltd
• Subjects: Computational physics; Dielectric materials; Electrostatic interaction; Electrostatics; Embedded systems; Galerkin method; Integral equations; Many-body; Mathematical models; Numerical analysis; Numerical methods; Polarization; Simulation; Spherical harmonics; Static electricity; Surface charge; Polarization; Surface charge; Dielectric materials; Electrostatic interaction; Many-body
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2018.06.015

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. •Numerically efficient solution to the problem of calculating electrostatic interactions between many dielectric particles is presented.•The method is general as it treats systems containing an arbitrary number of particles of any size, charge, dielectric constant.•The algorithmic complexity is reduced to linear scaling with respect to the number of particles.•The effect of polarization at short separations on the electrostatic force is considered.•The method is tested by the accurate estimations of the Madelung energy and constant of halite lattice.