Comparison of efficient techniques for the simulation of dielectric objects in electrolytes

Abstract

We review two recently developed efficient approaches for the numerical evaluation of the electrostatic polarization potential in particle-based simulations. The first is an image-charge method that can be applied to systems of spherical dielectric objects and provides a closed-form solution of Poisson's equation through multiple image-charge reflections and numerical evaluation of the resulting line integrals. The second is a boundary-element method that computes the discretized surface bound charge through a combination of the generalized minimal residual method (GMRES) and a fast Ewald solver. We compare the accuracy and efficiency of both approaches as a function of the pertinent numerical parameters. We demonstrate use of the image-charge method in a Monte Carlo simulation using the Barnes–Hut octree algorithm and the boundary-element method in a molecular dynamics simulation using the Particle–Particle Particle–Mesh (PPPM) Ewald method, and present numerical results for the ensemble-averaged induced force between two spherical colloids immersed in an electrolyte.