Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics (Communications in Computational Physics, 2020)
Volume-preserving algorithms (VPAs) for the charged particles dynamics ispreferred because of their long-term accuracy and conservativeness for phase spacevolume. Lie algebra and the Baker-Campbell-Hausdorff (BCH) formula can be usedas a fundamental theoretical tool to construct VPAs. Using the Lie algebra structure ofvector fields, we split the volume-preserving vector field for charged particle dynamicsinto three volume-preserving parts (sub-algebras), and find the corresponding Lie subgroups.Proper combinations of these subgroups generate volume preserving, secondorder approximations of the original solution group, and thus second order VPAs. Thedeveloped VPAs also show their significant effectiveness in conserving phase-spacevolume exactly and bounding energy error over long-term simulations.