Efficient solution of Poisson’s equation with free boundary conditions

Abstract

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.