Derivation and efficient implementation of the fast multipole method

摘要: The fast multipole method (FMM) of Greengard evaluates Coulomb interactions point charges with computational requirements that increase linearly the number particles. In this work, central transformations FMM are obtained in a very compact manner from simple algebraic manipulations two addition theorems. intermediate and Taylor expansions defined differently previous work to yield simplified more efficient transformations. Error estimates due effect truncation use transformation operator. Efficient implementation for potential forces is discussed, calculations presented probe accuracy performance method.