论文标题
双图：一种保存结构的方法，用于离散躺椅
Dual PIC: a structure preserving method for discretizing Lie-Poisson brackets
论文作者
论文摘要
我们考虑了由Lie-Poisson Brackets产生的Hamiltonian现场理论的一般离散策略，我们称之为双PIC（DPIC）。该方法涉及规定动态变量的两个不同的离散表示，它们被限制为流动的Casimir不变，以通过在整个模拟中通过L2投影相互重合。这允许人们利用每个离散表示的相对优势。我们首先描述了应用于一般的Lie-Poisson系统的DPIC，然后提供说明性示例：二维涡度方程的离散化和Vlasov-Poisson方程。
We consider a general discretization strategy for Hamiltonian field theories generated by Lie-Poisson brackets which we call dual PIC (DPIC). This method involves prescribing two different discrete representations of the dynamical variable which are constrained as a Casimir invariant of the flow to coincide with one another via an L2 projection throughout the entire simulation. This allows one to leverage the relative advantages of each discrete representation. We begin by describing DPIC as applied to a general Lie-Poisson system and then provide illustrative examples: the discretization of the two-dimensional vorticity equations and the Vlasov-Poisson equation.
