Weak scaling of parallel FMM vs. FFT up to 4096 processes

The FMM (fast multipole method) is used as the numerical engine in a vortex method fluid solver, simulating decaying isotropic turbulence. The reference method for this application is the pseudo-spectral method, which uses FFT as the numerical engine.

Given the communication pattern of FFT, only 14% parallel efficiency is obtained with the spectral method on 4096 processes (no GPU acceleration). The parallel efficiency of the FMM-based solver is 74% at 4096 processes (one GPU per MPI process, 3 GPUs per node). It is important to note that the results correspond to the full-application codes, not just the FMM and FFT algorithms.