Comparing the treecode with FMM on GPUs for vortex particle simulations of a leapfrogging vortex ring

We compare the performance of the treecode and the fast multipole method (FMM) on GPUs. These fast algorithms are used to accelerate a vortex particle simulation of two leapfrogging vortex rings. The performance of the treecode and FMM depends strongly on the number of particles, type of hardware, distribution of particles, and the required accuracy. Our results demonstrate that for the accuracy that is required in vortex method simulations the crossover point between the treecode and FMM is around N = 3000 on the CPU. On the GPU, the treecode is able to achieve more acceleration than the FMM, and no clear crossover point is observed.