For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The possibly infinite-dimensional system under consideration possesses a Hamiltonian function, which represents an energy in the system and is conserved or dissipated along solutions. The numerical scheme is energy-consistent in the sense that the Hamiltonian of the approximate solutions at time grid points behaves accordingly. This structure preservation property is achieved by specific design of a continuous Petrov-Galerkin (cPG) method in time. It coincides with standard cPG methods in special cases, in which the latter are energy-consistent. Examples of port-Hamiltonian ODEs and PDEs are presented to visualize the framework. In numerical experiments the energy consistency is verified and the convergence behavior is investigated.

翻译：针对一类广义非线性端口-哈密顿系统，我们提出了一种具有特定结构保持性质的高阶时间离散格式。所考虑的潜在无限维系统具有哈密顿函数，该函数代表系统中的能量，并沿解保持不变或耗散。该数值格式在时间网格点上近似解的哈密顿行为与其一致，因此具有能量相容性。这一结构保持性质通过时间上连续Petrov-Galerkin（cPG）方法的特定设计实现。在特殊情况下，该格式与标准cPG方法一致，且后者在此情形下具有能量相容性。通过端口-哈密顿常微分方程与偏微分方程实例展示该框架。数值实验中验证了能量相容性并研究了收敛行为。