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The port-Hamiltonian approach presents an energy-based modeling of dynamical systems with energy-conservative and energy-dissipative parts as well as an interconnection over the so-called ports. In this paper, we apply an operator splitting…

Numerical Analysis · Mathematics 2023-04-05 Andreas Frommer , Michael Günther , Björn Liljegren-Sailer , Nicole Marheineke

Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…

Numerical Analysis · Mathematics 2025-01-14 Jan Lorenz , Tom Zwerschke , Michael Günther , Kevin Schäfers

A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no…

Numerical Analysis · Mathematics 2023-09-26 Andreas Bartel , Michael Günther , Birgit Jacob , Timo Reis

In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints without altering them. This paper…

Numerical Analysis · Mathematics 2024-04-23 Andreas Bartel , Malak Diab , Andreas Frommer , Michael Günther , Nicole Marheineke

A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…

Functional Analysis · Mathematics 2023-02-03 Bálint Farkas , Birgit Jacob , Timo Reis , Merlin Schmitz

In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion…

Numerical Analysis · Mathematics 2017-06-28 Elena Celledoni , Eirik Hoel Høiseth

Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…

Dynamical Systems · Mathematics 2023-09-01 Andreas Bartel , Malak Diab , Andreas Frommer , Michael Günther

We consider infinite dimensional port-Hamiltonian systems. Based on a power balance relation we introduce the port-Hamiltonian system representation where we pay attention to two different scenarios, namely the non-differential operator…

Optimization and Control · Mathematics 2013-08-07 Markus Schöberl , Andreas Siuka

Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale…

Numerical Analysis · Mathematics 2015-03-17 Serkan Gugercin , Rostyslav V. Polyuga , Christopher Beattie , Arjan van der Schaft

In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in…

Computational Engineering, Finance, and Science · Computer Science 2023-04-26 Vladimir Salnikov , Antoine Falaize , Daria Loziienko

The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly…

Dynamical Systems · Mathematics 2025-11-26 Matthias Ehrhardt , Michael Günther , Daniel Ševčovič

Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…

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…

Numerical Analysis · Mathematics 2026-01-06 Philipp L. Kinon , Riccardo Morandin , Philipp Schulze

It is well known that linear and non-linear dissipative port-Hamiltonian systems in finite dimensions admit an energy balance, relating the energy increase in the system with the supplied energy and the dissipated energy. The integrand in…

Analysis of PDEs · Mathematics 2024-05-29 Friedrich M. Philipp

Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…

Optimization and Control · Mathematics 2024-12-20 Sarah-Alexa Hauschild , Nicole Marheineke , Volker Mehrmann

Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method…

Numerical Analysis · Mathematics 2025-07-21 Yuwei Geng , Lili Ju , Boris Kramer , Zhu Wang

In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…

Numerical Analysis · Mathematics 2020-08-20 Yalchin Efendiev , Petr N. Vabishchevich

This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in…

Numerical Analysis · Mathematics 2016-01-05 Saifon Chaturantabut , Chris Beattie , Serkan Gugercin

The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…

Dynamical Systems · Mathematics 2022-01-19 Volker Mehrmann , Benjamin Unger

Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…

Numerical Analysis · Mathematics 2023-10-10 Anand Srinivasan , Jose E. Castillo
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