FLUPS: a Fourier-based Library of Unbounded Poisson Solvers

Abstract

A Fourier-based Library of Unbounded Poisson Solvers (FLUPS) for 2-D and 3-D homogeneous distributed grids is presented. It is designed to handle every possible combination of periodic, symmetric, semi-unbounded and fully unbounded boundary conditions for the Poisson equation. FLUPS leverages a dedicated implementation of 3-D Fourier transforms to solve the Poisson equation using Green's functions, in a fast and memory-efficient way. Several Green's functions are available, optionally with explicit regularization or using Lattice Green Functions, and provide verified convergence orders from 2 to 6. The algorithm depends on the FFTW library to perform 1-D transforms, while MPI communications enable the required remapping of data in memory. For the latter operation, a first available implementation resorts to the standard all-to-all routines. A second implementation, featuring non-blocking and persistent pointto-point communications, is however shown to be more efficient in a majority of cases and especially while taking advantage of the shared memory parallelism with OpenMP. The scalability of the algorithm, aimed at massively parallel architectures, is demonstrated up to 73 720 cores. The results obtained with three different supercomputers show that the weak efficiency remains above 40% and the strong efficiency above 30% when the number of cores is multiplied by 16, for typical problems. These figures are slightly better than those expected from a third party 3-D FFT tool, with which a 20% longer execution time was also measured on average. From the outside, the solving procedure is fully automated so that the user benefits from the optimal performances while not having to handle the complexity associated with memory management, data mapping and Fourier transform computation. The parallel code is available under GPLv3 license at github.com/vortexlab-uclouvain/flups.