Multiscale Finite Element Formulations for 2D/1D Problems

Approaches for multiscale finite element methods (MSFEM) are proposed which are essentially more efficient while maintaining the accuracy of past 2D/1D approaches. They are based on a magnetic vector potential or a current vector potential. Known currents in conductors are replaced by their Biot-Savart-fields. Boundary conditions allow planes of symmetry. All presented approaches consider eddy currents and preserve the edge effect. A segment of a fictitious electrical machine has been studied to demonstrate the accuracy and the low computational costs of the 2D/1D MSFEMs.