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Electromagnetic Port Boundary Conditions: Topological and Variational Perspective

by R. Hiptmair and J. Ostrowski

(Report number 2020-27)

Abstract
We present a comprehensive and variational approach to the coupling of electromagnetic field models with circuit-type models. That coupling relies on integral non-local 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 non-bounding cycles studied in algebraic topology and they respect electromagnetic power balance laws. We obtain two dual variational formulations, called \(\mathbf{E}\)-based and \(\mathbf{H}\)-based, which provide a foundation for finite-element Galerkin discretization.

Keywords: field-circuit coupling, (M)ECE models, relative co-homology, electric and magnetic ports, finite elements

@Techreport{HO20_900,
  author = {R. Hiptmair and J. Ostrowski},
  title = {Electromagnetic Port Boundary Conditions: Topological and Variational Perspective},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2020-27},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-27.pdf },
  year = {2020}
}

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