Generalization of the Barnes-Hut algorithm for the Helmholtz equation in three dimensions

The Barnes-Hut algorithm originally developed for O(N log N) solution of the iV-body problem with the Laplace kernel is generalized to the case of the scalar Helmholtz kernel in three dimensions. Analogous to the center-of-charge concept used in the static algorithm, a center-of-radiation (CoR) is associated with each box of the hierarchically partitioned space enclosing the sources of interest. The algorithm is applicable to the acceleration of electromagnetic interactions between sources confined to electrically small volumes. The method may be used in conjunction with the high-frequency fast multipole method (FMM) to eliminate its low-frequency breakdown.