Multiscale fast summation of long‐range charge and dipolar interactions

Here we present a linear order multiscale method for the fast summation of long range forces in a system consisting of a large number of charge and dipolar particles. For a N‐body system, our algorithm requires an order of work that is proportional to O(N), in comparison to order O(N2) of the direct pairwise computation. Our method is demonstrated on two‐dimensional homogeneous point‐charge and dipolar systems, and a combined heterogeneous particle system, for the calculation of the induced electrostatic potential and energy. The electrostatic interaction is decomposed into a local part and a smooth part. The method thus, has several potential advantages over other O(N log N) or O(N) techniques, especially for calculation with moving particles or implicit charges locations. This approach is beneficial to large‐scale problems such as molecular statics, molecular dynamics, equilibrium statistics (Monte‐Carlo simulations), molecular docking, and in areas such as magnetism and astrophysics. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 717–731, 2001