A comparison between Fast Multipole Algorithm and Tree Code to evaluate Coulomb forces in 3-D

We present tests of comparison between our versions of the Fast Multipole Algorithm (FMA) and the tree-code to evaluate gravitational forces in particle systems. We have optimized Greengard’s original version of FMA allowing for a more efficient criterion of well-separation between boxes, to improve the adaptivity of the method (which is very important in highly inhomogeneous situations) and to permit the smoothing of gravitational interactions. The results of our tests indicate that the tree-code is 2–4 times faster than the FMA for clumped distributions and 3–9 times for homogeneous distributions, at least in the interval of N here investigated (N · 2 ¢ 105) and at the same level of accuracy (error»10¡3). This order of accuracy is generally considered as the best compromise between CPU-time consumption and precision for astrophysical simulations. Moreover, the claimed linear dependence on N of the CPU-time of the FMA is not confirmed and we give a “theoretical” explanation for that.