Author(s)

ALEXANDRA KOLGANOVA, ILIA MARCHEVSKY, EVGENIYA RYATINA

Abstract

New modification of the fast algorithm based on the Barnes–Hut (BH) and fast multipole method (FMM) is developed for the problem of velocities calculation in vortex particle method. It provides a quasilinear computational complexity and allows for the accuracy flexible adjustment, similar to the classic Barnes–Hut method. Four schemes are developed with a different number of terms being held in multipole and local expansions. All the necessary formulae are presented, expressed in terms of operations with complex numbers. If extremely high accuracy is not required, the proposed algorithm is more efficient in comparison to the traditional FMM methods.

Keywords

fast algorithm, n-body problem, vortex method, the Barnes–Hut algorithm, multipoles