High-accuracy minimum relaxation N-body simulations using orthogonal series force computation

This report describes a modification of orthogonal function Poisson solver for n body simulations that minimize relaxation caused by small particle number fluctuations. With the standard algorithm, the noise leading to relaxation can e reduced by making the expansion basis similar to the particle distribution and by carefully choosing the maximum order in the expansion. The proposed algorithm accomplishes both task simultaneously while the simulation is running. This procedure is asymptotically equivalent to expanding in an orthogonal series which is matched to the distribution to start and truncating a low order. Because the modified algorithm adapts to a time evolving distribution, it has advantage over a fixed basis. The required changes to the standard algorithm are minor and do not affect its overall structure or scalability. Tests show that the overhead in CPU time is small in practical applications. The decrease in relaxation rate is demonstrated for both axisymmetric and non axisymmetric system and the robustness of the algorithm is demonstrated by following the evolution of unstable generalized polytropes. Finally the empirically based moment analysis which leads to the uncorrelated basis is an ideal tool for investigating structure and modes in n body simulations and an examples is provided