Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method

Gnedin, Nickolay Y.

doi:10.3847/1538-4365/ab2d24

Title: Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method

Journal Article · 23 July 2019 · The Astrophysical Journal. Supplement Series (Online)

DOI: https://doi.org/10.3847/1538-4365/ab2d24 · OSTI ID:1545079

Gnedin, Nickolay Y. ^[1]

Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Univ. of Chicago, IL (United States)

I observe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a “gridlet”) of effective masses. The effective masses on a gridlet are set from the requirement that the multipole moments of the FMM cells are reproduced exactly, thus preserving the accuracy of the gravitational field representation. The measurement of the gravitational field from a multipole expansion can then be computed for all multipole orders simultaneously, with a single Fast Fourier Transform, significantly reducing the computational cost at a given value of the required accuracy. The described approach belongs to the class of “kernel independent” variants of the FMM method and works with any Green function.

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Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-07CH11359

OSTI ID:: 1545079

Report Number(s):: arXiv:1906.10734; FERMILAB-PUB-19-277-A; 1741462

Journal Information:: The Astrophysical Journal. Supplement Series (Online), Vol. 243, Issue 2; ISSN 1538-4365

Publisher:: American Astronomical Society/IOPCopyright Statement

Country of Publication:: United States

Language:: English

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