The Continuous Fast Multipole Method

The FMM has subsequently been applied to problems in astrophysics, plasma physics, molecular dynamics, fluid dynamics, partial differential equations and numerical complex analysis. The FMM was generalized to handle continuous distributions (forming the Continuous FMM, CFMM) in 1994 by White et al. [182,157] after making several improvements to the original FMM [180,183,184]. The main change was the introduction of a well-separated index, describing the distance required before interactions can be calculated via multipoles. This index depends on the diffuseness of the charge distributions involved. Over the last few years CFMM has become a very mature algorithm, and the Q-CHEM implementation is now a highly optimized, efficient code.