论文标题
Yang-Mills方程的多面体离散DE RHAM数值方案
A polyhedral discrete de Rham numerical scheme for the Yang-Mills equations
论文作者
论文摘要
我们使用离散的DE RHAM（DDR）序列的lie代数值扩展（DDR）序列的Yang-Mills方程的3+1公式的离散化，从而确切地保留了非线性约束。与麦克斯韦的方程式相反，在麦克斯韦的方程中，类似约束仅取决于再现连续de rham序列的某些复杂特性，而非线性约束的保留依赖于扬麦则取决于受约束的配方，以前在[10]中提出。 DDR方法的完全离散的性质需要设计适合离散空间的非线性术语的适当构造，并需要复制$ l^2 $ profoduct的关键advariance属性。然后，我们证明了一些能量估计，并基于此方案提供了3D数值模拟的结果。
We present a discretisation of the 3+1 formulation of the Yang-Mills equations in the temporal gauge, using a Lie algebra-valued extension of the discrete de Rham (DDR) sequence, that preserves the non-linear constraint exactly. In contrast to Maxwell's equations, where the preservation of the analogous constraint only depends on reproducing some complex properties of the continuous de Rham sequence, the preservation of the non-linear constraint relies for the Yang-Mills equations on a constrained formulation, previously proposed in [10]. The fully discrete nature of the DDR method requires to devise appropriate constructions of the non-linear terms, adapted to the discrete spaces and to the need for replicating the crucial Ad-invariance property of the $L^2$-product. We then prove some energy estimates, and provide results of 3D numerical simulations based on this scheme.
