Commutator-based operator splitting for linear port-Hamiltonian systems

The port-Hamiltonian approach offers a modeling of dynamic systems with an energy-conserving and a dissipative part. Port-Hamiltonian (pH) systems are passive. That means no energy can be generated within the system. A passive system cannot store more energy than it receives. The exact solution of the pH system fulfills the dissipation inequality. In this paper, we deal with operator splitting that considers the energy-conserving and dissipative parts separately. We aim at high-order splitting schemes that preserve the dissipation inequality. Fourth-order methods for linear pHs-ODE are derived and an extension to sixth-order methods is discussed.