FFT, FMM, or Multigrid? A comparative Study of State Of the Art Poisson Solvers for Uniform and Nonuniform Grids in the Unit Cube
From molecular dynamics and quantum chemistry, to plasma physics and computational astrophysics, Poisson solvers in the unit cube are used in many applications in computational science and engineering. In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the fast Fourier transform (FFT) the fast multipole method (FMM) the geometric multigrid (GMG) and algebraic multigrid (AMG) Our focus is on solvers supporting high order, highly nonuniform discretizations. To allow comparisons with standard libraries we also compare adaptive solvers with solvers specialized for problems on regular grids, that is, FFT and regular stencil multigrid, since both are very popular algorithms for several practical applications. For the multigrid, we use the finite element variant of a high performance geometric multigrid (HPGMG) benchmark. In total we compare five different codes, three of which are developed in our group. Our FFT, GMG, and.
SIAM J. Sci. Comput.