论文标题
关于计算泊松几何学II：数值方法
On Computational Poisson Geometry II: Numerical Methods
论文作者
论文摘要
我们提出了十二种数值方法，用于评估泊松几何形状的对象和概念。我们描述了每种方法如何与示例一起使用，并说明其在代码中的执行方式。这些方法包括评估哈密顿量和模块化矢量场的方法，计算在串联和微量运算符下的图像，差分1形式的谎言括号，量规变换以及$ \ mathbf {r}^{3} $上的lie-poisson结构的正常形式。计算了我们每种方法的复杂性，我们在二维和三个方面的示例中包括实验验证。
We present twelve numerical methods for evaluation of objects and concepts from Poisson geometry. We describe how each method works with examples, and explain how it is executed in code. These include methods that evaluate Hamiltonian and modular vector fields, compute the image under the coboundary and trace operators, the Lie bracket of differential 1-forms, gauge transformations, and normal forms of Lie-Poisson structures on $\mathbf{R}^{3}$. The complexity of each of our methods is calculated, and we include experimental verifications on examples in dimensions two and three.
