Port-Hamiltonian Systems

Project description

The Collaborative Research Centre (CRC) pursues an interdisciplinary research programme aimed at advancing the mathematical understanding of port-Hamiltonian systems (pHS) through fundamental analytical insights as well as tailored novel techniques in numerics and optimization. The projects within the CRC combine ambitious research goals in a balanced mix — some with a clear path to realization, others carrying higher risk but offering particularly high potential for progress.

A central theme across the CRC is the pH-conforming modeling of dynamical systems, grounded in generalized concepts of energy, its preservation and dissipation. Since pH systems frequently arise as coupled multiphysics systems, these structural features must be both respected and leveraged throughout the simulation pipeline — from spatial and temporal discretization to the numerical kernels used in actual computations. Project Area B addresses these challenges, with a particular focus on structure-preserving discretization, multiphysics coupling, and scalable numerical methods for large-scale simulations.

Within this context, Project B06 develops, analyzes, and simulates coupled discrete multi-model descriptions of realistic electromagnetic field problems. Progress in this area is crucial for understanding electromagnetic compatibility in complex systems such as electric vehicles. In contrast to current approaches, B06 preserves the port-Hamiltonian structure when coupling network descriptions with various electromagnetic and thermal models, resulting in a genuinely stable overall system. After appropriate discretization, these coupled systems are also simulated numerically.

B06 is closely linked to other projects in Area B. Together with B01 and B02, it addresses the challenge of multiphysics coupling, where different software packages must be linked while maintaining structural consistency. The time discretization schemes developed and evaluated in B06 benefit from the iterative solvers created in B04 and B05, which are specifically designed to preserve or exploit structure-induced properties — ensuring computational efficiency even in large-scale settings.

Project-related publications