Accurate computation of the mutual interactions of N particles through electrostatic or gravitational potential has impeded progress in many areas of simulation science. The Fast Multipole Algorithm provides an efficient scheme for reducing computational complexity.
Citation:
John Board, Klaus Schulten, "The Fast Multipole Algorithm," Computing in Science and Engineering, vol. 2, no. 1, pp. 76-79, Jan./Feb. 2000, doi:10.1109/5992.814662