Structural Aspects of Electromagneto-Quasistatic Field Formulations of Darwin-Type Derived in the Port-Hamiltonian System Framework

Electromagneto-quasistatic (EMQS) field formulations allow to model resistive, capacitive, and inductive field effects while neglecting wave propagation. These field formulations are based on the Darwin-Ampére equation and yield different approximations of the full set of Maxwell's equations depending on the choice of additional equations. Various discrete EMQS formulations are analyzed using the port-Hamiltonian system framework. It is shown that only combinations of the Darwin-Ampere equation and the Maxwell continuity equation yield port-Hamiltonian differential-algebraic system of equations (pH-DAE) which implies their numerical stability, energy conservation related to a specific EMQS variant of the Hamiltonian and dissipativity results.