A Hierarchical O(N) Force Calculation Algorithm

A novel code for the approximate computation of long-range forces between N mutually interacting bodies is presented. The code is based on a hierarchical tree of cubic cells and features mutual cell–cell interactions which are calculated via a Cartesian Taylor expansion in a symmetric way, such that total momentum is conserved. The code benefits from an improved and simple multipole acceptance criterion that reduces the force error and the computational effort. For N≳104, the computational costs are found empirically to rise sublinearly with N. For applications in stellar dynamics, this is the first competitive code with complexity O(N); it is faster than the standard tree code by a factor of 10 or more.