Figure 11

Scaling of computational costs with N . Wall-clock time for the computation of the mutual gravitational forces between N particles drawn from a Plummer sphere. The FMM (full squares) is parameterised (see Table 2) to yield acceleration errors very similar to those of direct summation on GPUs using the sapporo library (open triangles, using a NVIDIA K20M GPU accelerator).Footnote

The timings for the sapporo library also include additional computations (nearest neighbour finding and neighbour listing). These contribute negligibly at large N, but at small N they are, together with latency on the GPU, responsible for the deviation of the observed complexity from $N^2$.

The direct summation on 16 CPUs (open squares) uses double precision and besides the accelerations also computes the gravitational potential and the scale f (equation (4)).