Explicit highorder noncanonical symplectic particleincell algorithms for VlasovMaxwell systems
Abstract
Explicit highorder noncanonical symplectic particleincell algorithms for classical particlefield systems governed by the VlasovMaxwell equations are developed. The algorithms conserve a discrete noncanonical symplectic structure derived from the Lagrangian of the particlefield system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with highorder interpolating differential forms for a cubic grid. The resulting timedomain Lagrangian assumes a noncanonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structurepreserving splitting method discovered by He et al. [preprint arXiv:1505.06076 (2015)], which produces five exactly soluble subsystems, and highorder structurepreserving algorithms follow by combinations. The explicit, highorder, and conservative nature of the algorithms is especially suitable for longterm simulations of particlefield systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave.
 Publication:

Physics of Plasmas
 Pub Date:
 November 2015
 DOI:
 10.1063/1.4935904
 arXiv:
 arXiv:1510.06972
 Bibcode:
 2015PhPl...22k2504X
 Keywords:

 Physics  Plasma Physics
 EPrint:
 doi:10.1063/1.4935904