2025/05/24 by Kinon, Philipp L., Morandin, Riccardo, Schulze, Philipp · 2 citations
#34A09 #65L80 #65P10 #70E55 #93C10 #Computational Engineering #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Finance #Numerical Analysis (math.NA) #Robotics (cs.RO) #Systems and Control (eess.SY) #and Science (cs.CE) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2505.18810
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient methods to the system class of nonlinear port-Hamiltonian differential-algebraic equations - as they emerge from the port- and energy-based modeling of physical systems in various domains. We introduce a novel numerical scheme tailored for semi-explicit differential-algebraic equations and further address more general settings using the concepts of discrete gradient pairs and Dirac-dissipative structures. Additionally, the behavior under system transformations is investigated and we demonstrate that under suitable assumptions port-Hamiltonian differential-algebraic equations admit a representation which consists of a parametrized port-Hamiltonian semi-explicit system and an unstructured equation. Finally, we present the application to multibody system dynamics and discuss numerical results to demonstrate the capabilities of our approach.