IFIP TC7 System Modeling and Optimization

High-order operator splitting methods for linear port-Hamiltonian systems

Aug 13, 2024, 11:30 AM

30m

Seminarraum 208 (Von-Melle-Park 8)

Minisymposium Contribution MS 03: Recent trends in control and numerics of port-Hamiltonian systems MS 03: Recent trends in control and numerics of port-Hamiltonian systems

Speaker

Marius Mönch (Trier University - Department IV)

Description

The lecture deals with numerical methods for solving port-Hamiltonian systems. The focus is on operator splitting methods. The aim is to derive high-order methods that preserve the port-Hamiltonian properties. Splitting methods with an order of three and higher have negative step sizes. As a result, the dissipation inequality is no longer preserved. Remedy create force-gradient methods. With the help of force-gradient terms, it is possible to construct fourth-order methods that only have positive step sizes and satisfy the dissipation inequality. Finally, the case of sixth order methods is explained.