Efficient solution of Poisson’s equation with free boundary conditions

• DOI: 10.1063/1.2335442
• Publication Date: 2006-08-17T22:05:57Z
• Authors: Luigi Genovese; Thierry Deutsch; Alexey Neelov; Stefan Goedecker; Gregory Beylkin
• Keywords: Condensed Matter - Materials Science; 0103 physical sciences; [PHYS.COND.CM-MS]Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci]; Materials Science (cond-mat.mtrl-sci); FOS: Physical sciences; 01 natural sciences

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(NlogN) 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.