A fast multipole method for stellar dynamics
Abstract
The approximate computation of all gravitational forces between N interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than ? ( N) operations. FMM groups particles into spatially bounded cells and uses cellcell interactions to approximate the force at any position within the sink cell by a Taylor expansion obtained from the multipole expansion of the source cell. By employing a novel estimate for the errors incurred in this process, I minimise the computational effort required for a given accuracy and obtain a wellbehaved distribution of force errors. For relative force errors of ∼10^{7}, the computational costs exhibit an empirical scaling of ∝ N ^{0.87}. My implementation (running on a 16 core node) outperforms a GPUbased direct summation with comparable force errors for.
 Publication:

Computational Astrophysics and Cosmology
 Pub Date:
 September 2014
 DOI:
 10.1186/s4066801400017
 arXiv:
 arXiv:1405.2255
 Bibcode:
 2014ComAC...1....1D
 Keywords:

 Astrophysics  Instrumentation and Methods for Astrophysics;
 Physics  Computational Physics
 EPrint:
 21 pages, 15 figures, accepted for publication in Journal for Computational Astrophysics and Cosmology