Stability of Transient Coupled Multi-Model Discrete Electromagnetic Field Formulations Using the Port-Hamiltonian System Framework

The port-Hamiltonian system (pHS) framework established for coupled system formulations in multi-model and multi-physics problems considers physical model formulations either in a continuous setting as sets of partial differential equations or, alternatively, in discrete variants as pH differential-algebraic equations (pH-DAEs) [1]. The key to pHS formulations is that they are established with respect to energy conservation and dissipation inequalities. A typical $\mathrm{pH}-\mathrm{DAE}$ is given in the form