TY - JOUR
T1 - Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics
AU - Ruili Zhang, Jian Liu, Hong Qin, Yifa Tang, Yang He & Yulei Wang
JO - Communications in Computational Physics
VL - 5
SP - 1397
EP - 1408
PY - 2018
DA - 2018/04
SN - 19
DO - http://doi.org/10.4208/cicp.scpde14.33s
UR - https://global-sci.org/intro/article_detail/cicp/11135.html
KW - 
AB - <p style="text-align: justify;">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.</p>