高阶能量守恒线积分方法用于带电粒子动力学

离散线积分方法用于洛伦兹力系统

Discrete line integral method for the Lorentz force system

本文应用Boole离散线积分方法求解洛伦兹力系统，该系统可视为非规范哈密顿系统。方法对多项式哈密顿量度不超过4的系统精确守恒能量，其他情况下也能近似守恒。通过与Boris方法的对比实验，展示方法的能量守恒特性。

Hamiltonian PDEs的线积分解法

Line Integral solution of Hamiltonian PDEs

本文研究了利用能量守恒的线积分方法求解Hamiltonian偏微分方程的问题，通过半线性波方程、非线性薛定谔方程和Korteweg-de Vries方程展示该方法的主要特征。

一种用于带电粒子动力学的直接能量保持新方法

A novel directly energy-preserving method for charged particle dynamics

本文提出一种直接且精确保持能量的 CIDG-C 方法用于求解 Lorentz 力系统，数值实验证明其在能量保持方面优于 Boris 方法。

粒子在格点中的精确电荷守恒散集算法：几何视角

Exact Charge-Conserving Scatter-Gather Algorithm for Particle-in-Cell Simulations on Unstructured Grids: A Geometric Perspective

本文提出一种基于几何方法的精确电荷守恒散集算法，用于无结构网格的粒子-细胞模拟，通过离散微分形式实现电荷守恒，避免后处理步骤，提供简洁的散集表达式和几何解释。

Explicit Exactly Energy-conserving Methods for Hamiltonian Systems

For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each time step, or are explicit, but where the exact conservation property depends on the exact evaluation of an integral in continuous time. Under further restrictions, namely that the potential energy contribution to the Hamiltonian is non-negative, newer techniques based on invariant energy quadratisation allow for exact numerical energy conservation and yield…