Speaker
Description
In this talk, we present splitting methods for closed port-Hamiltonian systems, focusing on preserving their internal structure, particularly the dissipation inequality. Port-Hamiltonian systems are characterized by their ability to describe energy-conserving and dissipative processes. The physical properties are encoded in the algebraic structure of the system. Operator splitting takes advantageous of the decomposition of the underlying problem into subproblems of profoundly different behavior. Classical splitting schemes of order p≥3 involve negative step sizes. For time-irreversible systems, such as port-Hamiltonian systems with dissipation, the positivity of the step sizes is essential. Negative step sizes can be avoided by help of commutator-based methods. We introduce an energy-associated decomposition that exploits the system’s energy properties. Then, the numerical structure preservation depends crucially on the properties of the designed commutator. We set up skew-symmetric commutators for linear systems and discuss generalizations for non-linear systems. In particular, we present splitting schemes up to order four for special port-Hamiltonian systems. The proposed approaches are validated through theoretical analysis and numerical experiments.
