Lekner summation of dipolar interaction in quasi-two-dimensional simulations

The Lekner method for calculation of electrostatic interactions in periodically replicated simulation cells is extended to quasi-two-dimensional systems of particles with dipolar interactions. The electric ®eld, potential energy, forces and torques are expressed through rapidly converging series of modi®ed Bessel functions. The method contains no arbitrary parameters, and has no limitations on the simulation box width.