Abstract
We derive a rigorous analytical formalism and propose a numerical method for the quantitative evaluation of the electrostatic interactions between dielectric particles in an external electric field. This formalism also allows for inhomogeneous charge distributions, and, in particular, for the presence of pointlike charges on the particle surface. The theory is based on a boundary integral equation framework and yields analytical expressions for the interaction energy and net forces that can be computed in linear scaling cost, with respect to the number of interacting particles. We include numerical results that validate the proposed method and show the limitations of the fixed dipole approximation at small separation between interacting particles. The proposed method is also applied to study the stability and melting of ionic colloidal crystals in an external electric field.