Speaker
Description
Port-Hamiltonian systems are an extension of Hamiltonian systems that incorporate network structure and energy exchanges through ports, enabling the modeling of open, interconnected physical systems from various domains. The interconnection of network components often leads to differential-algebraic equations, which also include algebraic constraints, like in the case of Kirchhoff's laws. To ensure that these constraints are not violated, additional care is necessary when applying numerical methods to differential algebraic equations.
In this talk, we discuss the application of discrete gradient methods to nonlinear port-Hamiltonian descriptor systems, with a specific focus on the case of semi-explicit differential-algebraic equations. Discrete gradient methods are particularly suitable for the time discretization of port-Hamiltonian systems since they are structure-preserving regardless of the form of the Hamiltonian, unlike other common methods whose structure-preserving characteristics are limited to quadratic Hamiltonians, like the implicit midpoint rule. We also present numerical results to demonstrate the capabilities of our methods. This is joint work with Philipp L. Kinon (KIT) and Philipp Schulze (TU Berlin).
