Efficient solution of Poisson's equation with free boundary conditions
  Interpolating scaling functions give a faithful representation of a localized charge distribution by its values on a grid. For such charge distributions, using a Fast Fourier method, we obtain highly accurate electrostatic potentials for free boundary conditions at the cost of O(N log N) operations, where N is the number of grid points. Thus, with our approach, free boundary conditions are treated as efficiently as the periodic conditions via plane wave methods. 
Luigi Genovese, Thierry Deutsch, Alexey Neelov, Stefan Goedecker,   Gregory Beylkin