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Electromagnetic port boundary conditions: Topological and variational perspective
Author(s) -
Hiptmair Ralf,
Ostrowski Jörg
Publication year - 2020
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2839
Subject(s) - topology (electrical circuits) , discretization , electromagnetic field , boundary element method , galerkin method , magnetomotive force , coupling (piping) , finite element method , discontinuous galerkin method , magnetic field , physics , magnetic flux , mathematics , mathematical analysis , electrical engineering , engineering , mechanical engineering , quantum mechanics , thermodynamics
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.