Volume 19, Issue 5
Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics

Ruili Zhang, Jian Liu, Hong Qin, Yifa Tang, Yang He & Yulei Wang

Commun. Comput. Phys., 19 (2016), pp. 1397-1408.

Published online: 2018-04

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  • 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.

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@Article{CiCP-19-1397, author = {}, title = {Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {5}, pages = {1397--1408}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.33s}, url = {http://global-sci.org/intro/article_detail/cicp/11135.html} }
TY - JOUR T1 - Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics JO - Communications in Computational Physics VL - 5 SP - 1397 EP - 1408 PY - 2018 DA - 2018/04 SN - 19 DO - http://dor.org/10.4208/cicp.scpde14.33s UR - https://global-sci.org/intro/article_detail/cicp/11135.html KW - AB -

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.

Ruili Zhang, Jian Liu, Hong Qin, Yifa Tang, Yang He & Yulei Wang. (2020). Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics. Communications in Computational Physics. 19 (5). 1397-1408. doi:10.4208/cicp.scpde14.33s
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