Long-ranged electrostatics from local algorithms

We show how to generate the long-ranged Coulomb interaction between pairs of particles with the help of an auxiliary field evolving with local dynamics. This allows one to simulate systems containing electric charges without ever calculating the Coulomb potential or solving Poisson's equation. The methods require the imposition of Gauss's law as a dynamical constraint on the auxiliary field. The local approach is particularly suited to treat implicit solvent models of dielectric media as well as Poisson-Boltzmann models of solutions. Generalizations to nonperiodic boundary conditions as well as practical aspects of the implementation are also reviewed.