Storage reduction method for fast multipole field calculations

A method for efficiently storing quantities used by the Fast Multipole Method (FMM) to perform field calculations is disclosed. This method takes advantage of the level structure used by the FMM. The disclosed method selects a particular level and, for each group in that level, calculates interactions with all far groups. The disclosed method does not repeat calculations for interaction of a similar distance for the same level. Rather, it references calculations previously made for the similar interaction, thereby eliminating the calculation and storage of information that is the same as information previously calculated and stored.