Subcycling of particle orbits in variational, geometric electromagnetic particle-in-cell methods

用于动理学等离子体模拟的超鲍里斯积分器

Hyper Boris integrators for kinetic plasma simulations

本文提出超Boris求解器族，通过子循环时间步长和各向异性电场回旋相位校正，将标准Boris方法扩展至高阶精度，以可承受计算成本实现∼(Δt/n)^N的数值误差。

Variational Formulation of Macro-Particle Models for Electromagnetic Plasma Simulations

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398, 2013], the discretization of the electromagnetic Low Lagrangian is performed via a reduction of the phase-space distribution function onto a collection of finite-sized macro-particles of arbitrary shape and discretization of field quantities onto a spatial grid. This approach may be used with both lab frame coordinates or moving window coordinates; the latte…

Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme

A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus, the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

利用弯曲单元求解电磁波的高阶超弱变分公式

A High-Order Ultra-Weak Variational Formulation for Electromagnetic Waves Utilizing Curved Elements

本文提出将曲面三角形单元引入并行超弱变分公式（ParMax）求解时谐Maxwell方程组，结合总场/散射场与传输条件处理电阻薄片，并通过大尺寸弯曲单元和低内存策略成功模拟飞机X波段散射，验证了其工业应用价值。

A classical field theory formulation for the numerical solution of time harmonic electromagnetic fields

Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the `curl-curl' equation for the fields. We present a variational formulation based on classical field theory. Borrowing from QED, we modify the Lagrangian by adding an implicit gauge-fixing term. Our formulation, in the language of differential geometry, shows that conventional edge elements should be replaced by the simpler nodal elements for time-harmonic problems. We demonstrate how this formulation, adhering to the deeper underlying symmetries of the four-dimensional…

Nonlinear Motion in Electromagnetic Fields via Multiscale Expansions

The consideration of dynamics of relativistic beams/particles is based on variational approach to rational (in dynamical variables) approximation for equations of motions. It allows to control contribution from each scale of underlying multiscales and represent solutions via exact nonlinear eigenmodes expansions. Our approach is based on methods provided possibility to work with well-localized bases in phase space and good convergence properties of the corresponding expansions.