open access

https://hdl.handle.net/2115/68384

A force evaluation free method to N-body problems: Binary interaction approximation

英語

PPPM

2016-03

Elsevier

Communications in Nonlinear Science and Numerical Simulation

32

273-284

We recently proposed the binary interaction approximation (BIA) to N-body problems, which, in principle, excludes the interparticle force evaluation if the exact solutions are known for the corresponding two-body problems such as the Coulombic and gravitational interactions. In this article, a detailed introduction to the BIA is given, including the error analysis to give the expressions for the approximation error in the total angular momentum and the total energy of the entire system. It is shown that, although the energy conservation of the BIA scheme is worse than the 4th order Hermite integrator (HMT4) for similar elapsed, or the wall-clock times, the individual errors in position and in velocity are much better than HMT4. The energy error correction scheme to the BIA is also introduced that does not deteriorate the individual errors in position and in velocity. It is suggested that the BIA scheme is applicable to the tree method, the particle–mesh (PM), and the particle–particle-particle–mesh (PPPM) schemes simply by replacing the force evaluation and the conventional time integrator with the BIA scheme.

学術雑誌論文

Accepted Manuscript

Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

1007-5704