求解洛伦兹力系统的一个任意高阶的能量守恒格式

本文旨在提出一种求解带电粒子系统的任意高阶能量守恒格式.在使用能量不变二次化方法将原始哈密顿能量泛函转化为一个二次形式后,辛龙格-库塔方法被用来构造了一种新的能量守恒格式来求解洛伦兹力系统.新格式不仅能保持能量守恒,而且可以达到任意高阶.通过与经典的Boris方法和另一个二阶能量守恒方法对比,数值实验验证了所提算法的显著优越性.     

A local energy-preserving scheme for Zakharov system

In this paper, we propose a local conservation law for the Zakharov system. The property is held in any local timespace region which is independent of the boundary condition and more essential than the global energy conservation law.Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose a local energy-preserving(LEP) scheme for the system. The merit of the proposed scheme is that the local energy conservation law can be conserved exactly in any time-space region. With homogeneous Dirchlet boundary conditions, the proposed LEP scheme also possesses the discrete global mass and energy conservation laws. The theoretical properties are verified by numerical results.     

LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KLEIN-GORDON-ZAKHAROV EQUATION

In this paper, using the concatenating method, a series of local structure-preserving algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multisymplectic algorithms, four local energy-preserving algorithms, four local momentumpreserving algorithms; of these, local energy-preserving and momentum-preserving algorithms have not been studied before. The local structure-preserving algorithms mentioned above are more widely used than the global structure-preserving algorithm...