MSFEM for the Linear 2D1D-Problem of Eddy Currents in Thin Iron Sheets

Abstract

A 2D/1D method to simulate the eddy currents in a single thin iron sheet is presented. It utilizes ideas of the multiscale method by decomposing the solution with respect to its dependence on the coordinate directions. Instead of the three dimensional domain, the eddy current problem is solved only on the two dimensional cross section of the sheet, with the behavior of the solution along the thickness being simulated via an expansion into polynomial shape functions. This greatly reduces the number and the coupling density of the degrees of freedom. A numerical example shows a satisfying accuracy for both the A and the T formulation.