Figure 8

Acceleration errors for improved FMM. Same as Figure 7 but for the multipole-acceptance criterion (16a) with ϵ=2\times {10}^{-7} (left) or (16b) with ϵ={10}^{-7} (right). The values for a and f are either taken from the direct-summation run (black), or obtained by low-oder FMM (red, see Section 5.4.2). In all cases the computational effort is similar to that of the FMM run shown in Figure 7 (since a\le f criterion (16a) gives a tighter constraint than (16b) and hence requires larger ϵ for the same computational effort).