论文标题
弗拉索夫 - 波森方程的哈密顿粒子粒子方法
Hamiltonian Particle-in-Cell methods for Vlasov-Poisson equations
论文作者
论文摘要
在本文中，弗拉索夫 - 波森系统的粒子中算法是根据其泊松支架结构提出的。泊松方程是通过有限元方法求解的，其中采用适当的有限元空间来确保半消失的系统具有明确定义的离散泊松支架结构。然后，通过分解哈密顿函数，将分裂方法应用于半差异系统。事实证明，由此产生的离散是保存泊松支架。此外，该系统的保守量也得到了很好的保存。在数值实验中，我们使用呈现的数值方法来模拟各种物理现象。由于实用计算的巨大计算工作，我们采用了并行计算的策略。数值结果验证了新派生的数值离散效率。
In this paper, Particle-in-Cell algorithms for the Vlasov-Poisson system are presented based on its Poisson bracket structure. The Poisson equation is solved by finite element methods, in which the appropriate finite element spaces are taken to guarantee that the semi-discretized system possesses a well defined discrete Poisson bracket structure. Then, splitting methods are applied to the semi-discretized system by decomposing the Hamiltonian function. The resulting discretizations are proved to be Poisson bracket preserving. Moreover, the conservative quantities of the system are also well preserved. In numerical experiments, we use the presented numerical methods to simulate various physical phenomena. Due to the huge computational effort of the practical computations, we employ the strategy of parallel computing. The numerical results verify the efficiency of the new derived numerical discretizations.
