Electromagnetic port boundary conditions: Topological and variational perspective

Abstract

We present a comprehensive and variational approach to the coupling of electromagnetic field models with circuit‐type models. That coupling relies on integral nonlocal quantities like voltage and current for electric ports, magnetomotive force, and magnetic flux for magnetic ports, and linked currents and fluxes for “tunnels” in the field domain. These quantities are closely linked to nonbounding cycles studied in algebraic topology and they respect electromagnetic power balance laws. We obtain two dual variational formulations, called E‐based and H‐based, which provide a foundation for finite‐element Galerkin discretization. © 2020 John Wiley & Sons, Ltd