Ewald summation techniques in perspective: A survey

The simulation of large macromolecular systems has been and remains a challenging problem. There is a general presumption that simulations carried in periodic boundary conditions (PBC) are often the most appropriate to suppress boundary effects. To this end, Ewald summation has been employed to handle long ranged interactions in PBC. There has been a great deal of research targeted at improving the efficiency of Ewald summation, an O(N-2) algorithm in its traditional formulation, where N is the number of particles in the system. This paper reviews Ewald summation techniques by surveying conventional as well as state of the art efficient methods. Conventional methods, such as tabulation and approximation, are first re-examined along with an O(N-3/2) method. Fourier-based approaches which have reduced the complexity to O(N log(N)) are presented. Multipole expansion techniques, suggested as an alternative to Ewald sums, are reviewed and compared to Fourier methods. The computational efficiency of these new methods facilitates longer, larger and more realistic simulations.