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

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.