A Scalable Fast Multipole Method Poisson Solver for the RAMSES code: I. Unigrid Algorithm

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ID: 318987
2026
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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 solver (MG) — an iterative method that requires multiple V-cycles through a multi-resolution 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 around 30 times more floating-point operations than MG, its higher arithmetic intensity leads to comparable performance and better scalability relative to MG.
Reference Key
openalex_W7166292705 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Jun-Young Lee, Romain Teyssier
Journal monthly notices of the royal astronomical society
Year 2026
DOI
10.1093/mnras/stag1241
URL
https://doi.org/10.1093/mnras/stag1241
Keywords Keywords not found

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