New Applications of Integral Equation Methods for Solvation Continuum Models: Ionic Solutions and Liquid Crystals

We present a new method for solving numerically the equations associated with solvation continuum models, which also works when the solvent is an anisotropic dielectric or an ionic solution. This method is based on the integral equation formalism. Its theoretical background is set up and some numerical results for simple systems are given. This method is much more effective than three-dimensional methods used so far, like finite elements or finite differences, in terms of both numerical accuracy and computational costs.