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A force evaluation free method to N-body problems: Binary interaction approximation
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Title: | A force evaluation free method to N-body problems: Binary interaction approximation |
Authors: | Oikawa, S. Browse this author →KAKEN DB |
Keywords: | N-body problem | Binary interaction approximation (BIA) | Error analysis | Energy error correction | Pair-wise variable step size | Parallel computation | Tree method | PPPM |
Issue Date: | Mar-2016 |
Publisher: | Elsevier |
Journal Title: | Communications in Nonlinear Science and Numerical Simulation |
Volume: | 32 |
Start Page: | 273 |
End Page: | 284 |
Publisher DOI: | 10.1016/j.cnsns.2015.08.021 |
Abstract: | 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. |
Rights: | © 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/ | https://creativecommons.org/licenses/by-nc-nd/4.0/ |
Type: | article (author version) |
URI: | http://hdl.handle.net/2115/68384 |
Appears in Collections: | 工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 及川 俊一
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