论文标题
结构保存一维港口系统的不连续的盖金近似
Structure preserving discontinuous Galerkin approximation of one-dimensional port-Hamiltonian systems
论文作者
论文摘要
在本文中，我们介绍了使用不连续的Galerkin（DG）方法的两种保护定律的线性一维港口港口（pH）系统的结构保存离散化。我们回想起基于计算域的细分的DG离散过程，该过程是一个元素弱公式，最多可以通过零件进行两个集成，以及使用几个数值通量的元素互连。我们介绍了元素模型的互连，该元素模型是保守（未稳定）数值通量的幂，并设置了由此产生的全局pH状态空间模型。我们讨论获得的模型的特性，包括通量稳定参数对光谱的影响。最后，我们显示了具有不同参数的模拟，用于边界控制的线性双曲系统。
In this article, we present the structure-preserving discretization of linear one-dimensional port-Hamiltonian (PH) systems of two conservation laws using discontinuous Galerkin (DG) methods. We recall the DG discretization procedure which is based on a subdivision of the computational domain, an elementwise weak formulation with up to two integration by parts, and the interconnection of the elements using several numerical fluxes. We present the interconnection of the element models, which is power preserving in the case of conservative (unstabilized) numerical fluxes, and we set up the resulting global PH state space model. We discuss the properties of the obtained models, including the effect of the flux stabilization parameter on the spectrum. Finally, we show simulations with different parameters for a boundary controlled linear hyperbolic system.
