论文标题
用于边界控制的双曲线或抛物线PDE的港口港口系统的数值近似
Numerical approximation of port-Hamiltonian systems for hyperbolic or parabolic PDEs with boundary control
论文作者
论文摘要
由于哈米尔顿港的形式主义，我们考虑了为边界控制偏微分方程（PDES）解决结构的离散方法的设计。我们首先提供了一个新颖的一般结构，该结构是无限维港口系统（PHS）的新型一般结构，该结构可直接适用分区有限元方法（PFEM）。提出的策略应用于PDE的抽象多维线性双曲线和抛物线系统。然后，我们显示了基于波动方程，Mindlin方程和热方程在此统一框架内的教学模型问题。其次，我们介绍了为无限维pH的数值模拟开发的正在进行的项目SCRIMP（多物理中的相互作用的模拟和控制）。 Scrimp特别依赖Fenics开源计算平台来进行有限元空间离散化。最后，我们通过仔细解释方法来说明如何在本框架内解决所考虑的模型问题。作为额外的支持，可以使用伴侣互动jupyter笔记本。
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly we introduce the ongoing project SCRIMP (Simulation and ContRol of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.
