Multiscale finite element formulations for 2D/1D problems

Abstract

Multiscale finite element methods for 2D/1D problems have been studied in this work to demonstrate their excellent ability to solve the eddy current problem in a single iron sheet of electrical machines. We believe that these methods are much more efficient than conventional 3D finite element methods and just as accurate. The 2D/1D multiscale finite element methods are based on a magnetic vector potential or a current vector potential. Known currents for excitation can be replaced by the Biot-Savart-field. Boundary conditions allow to integrate planes of symmetry. All approaches consider eddy currents, an insulation layer and preserve the edge effect. A segment of a fictitious electrical machine has been studied to demonstrate all above options, the accuracy and the low computational costs of the 2D/1D multiscale finite element methods. Numerous simulations are presented. Direct and iterative solvers were investigated to reliably solve the system of equations from 2D/1D MSFEMs.