Multiscale Finite Element Formulations for the Eddy Current Problem in Open Magnetic Circuits

The multiscale finite element method (MSFEM) has shown its high potential for the simulation of the eddy current problem in closed magnetic circuits. This work presents two formulations to extend the MSFEM to open magnetic circuits. To this end, a three dimensional eddy current problem with the
$A$
and the
$T,\Phi\text{-}\Phi$
formulation and linear material relations has been studied. Numerical results demonstrate the accuracy of the presented methods.