Electrostatic interactions between dielectric objects are complex and of a many-body nature, owing to induced surface bound charge. We present a collection of techniques to simulate dynamical dielectric objects. We calculate the surface bound charge from a matrix equation using the Generalized Minimal Residue method (GMRES). Empirically, we find that GMRES converges very quickly. Indeed, our detailed analysis suggests that the relevant matrix has a very compact spectrum for all non-degenerate dielectric geometries. Each GMRES iteration can be evaluated using a fast Ewald solver with cost that scales linearly or near-linearly in the number of surface charge elements. We analyze several previously proposed methods for calculating the bound charge, and show that our approach compares favorably.
