Work

A scalable fast multipole method Poisson solver for the ramses code – I. Unigrid algorithm

Year: 2026

Type: article

Abstract: ABSTRACT We present a scalable Poisson solver with $\mathcal {O}(N)$ complexity based on the fast multipole method (FMM) implemented in ramses. Our FMM constructs a hierarchy of FMM grids on top of the pre-existing Cartesian grid, which is used to compute the force for hydrodynamics or particle-mesh simulations. In contrast to the $\mathcal {O}(N)$ multigrid (MG) solver – an iterative method that requires multiple V-cycles through a multiresolution hierarchy of Cartesian grids – the FMM algorithm performs just one upward pass through the same hierarchy, during which multipole expansions are accumulated and shifted, followed by a single downward pass, in which local expansions are propagated. Numerical tests indicate that FMM attains accuracy comparable to that of MG for smooth potentials and is particularly well-suited for problems with isolated boundary conditions, since it avoids the approximate Dirichlet boundary conditions required by MG schemes. Although in theory FMM requires about 30 times more floating-point operations than MG, its higher arithmetic intensity leads to comparable performance and better scalability relative to MG.

Source: Monthly Notices of the Royal Astronomical Society

DOI: 10.1093/mnras/stag1241

Authors: Jun-Young Lee, Romain Teyssier

Institution: Princeton University

Language: English

Topic: Electromagnetic Scattering and Analysis

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,046

Funders: National Science Foundation, United States - Israel Binational Science Foundation