Dual magnetodynamic finite element formulations with natural definitions of global quantities for electric circuit coupling

Both general families of magnetodynamic formulations, i.e. h- and b-conform formulations, are studied in the frame of the finite element method, in 2D and 3D. These dual formulations are respectively weak forms of the Faraday and Ampere equations, and respectively use unknowns directly associated with the magnetic field h (e.g. magnetic field - magnetic scalar potential h-formulations) and with the magnetic flux density b (e.g. magnetic vector potential a-formulations).
When such formulations are applied to systems coupled with electric circuits, not only local quantities, characterizing the unknown field, are involved, but also electric global quantities, i.e. currents and voltages. The conducting regions carry- ing these global quantities can be of massive or stranded types, each type necessitating a formulation dependent treatment. The mathematical and numerical tools for naturally coupling local and global quantities are studied for all these variants, using edge and nodal coupled finite elements and efficient forms of source magnetic and electric fields. The results are circuit relations characterizing the con- ducting regions, i.e. relations relating currents and voltages.