Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics

Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics

Year:    2016

Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.scpde14.33s

Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1397–1408

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:   

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