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. K E Y W O R D S(M)ECE models, electric and magnetic ports, field-circuit coupling, finite elements, relative cohomology

Electric circuit element boundary conditions in the finite element method for full-wave passive electromagnetic devices

“…In [4] we used E strictly inside the domain and V solely on the boundary. During the reviewing process of [4], Hiptmair and Ostrowski released a relevant report published in [14] proving the interest for this subject. In [19] the same authors propose a FW FEM formulation coupled with circuits, with a strong emphasis on the stability of the field solution inside the domain at low frequencies.…”

Dual Full-Wave Formulations with Radiant Electric Circuit Element Boundary Conditions. Application to Monopole Antenna Modeling

“…The interest for the ECE BC subject is also proven in Scorretti (2021) where an impressive relevant reference list can be found. For the FW EM field regime, a sound and general theory for weak E-based and H-based formulations with electric and magnetic ports, for multiply connected domains and linear materials can be found in Hiptmair and Ostrowski (2021). In Ciuprina et al (2022) we showed how the E-based formulation, with an electric field strictly inside the domain and electric scalar potential on the boundary, can be implemented and used for parameter extraction.…”

“…In Ciuprina et al (2023) the Hbased formulation (with a magnetic field inside the domain) was discussed and used for standard ECE, without a radiant surface. We consider the H formulation proposed in Ciuprina et al (2023) is different from the one in Hiptmair and Ostrowski (2021) because in our formulation the time domain correspondent involves convolution integrals and the scalar potential is defined only on the boundary. Moreover, in our approach the topological analysis of the boundary is necessary, to find the cuts that make the magnetic scalar potential univalent, which is not needed in the E formulation.…”