Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics. (17th May 2016)

• Record Type: Journal Article
• Authors: Zhang, Ruili; Liu, Jian; Qin, Hong; Tang, Yifa; He, Yang; Wang, Yulei
• Is Part Of: Communications in computational physics. Volume 19:Number 5(2016:May)
• Page Start: 1397
• Page End: 1408
• Publication Date: 2016-05-17
• Subjects: 17B81, -- 22E70, -- 70H33, -- 70H40; Lie algebra, -- Lie group, -- volume-preserving algorithm, -- charged particles dynamics; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.scpde14.33s
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: Volume-preserving algorithms (VPAs) for the charged particles dynamics is preferred because of their long-term accuracy and conservativeness for phase space volume. Lie algebra and the Baker-Campbell-Hausdorff (BCH) formula can be used as a fundamental theoretical tool to construct VPAs. Using the Lie algebra structure of vector fields, we split the volume-preserving vector field for charged particle dynamics into three volume-preserving parts (sub-algebras), and find the corresponding Lie subgroups. Proper combinations of these subgroups generate volume preserving, second order approximations of the original solution group, and thus second order VPAs. The developed VPAs also show their significant effectiveness in conserving phase-space volume exactly and bounding energy error over long-term simulations.