A finite-element approach in order to avoid ill-conditioning in thin-sheet problems in frequency domain—Application to magneto-quasistatics

In this work, a new thin-sheet approach in the finite-element method is derived. The focus is on the condition number of the system matrix, namely, to keep this measure preferably independent of the thickness of the sheet. Constant sheet elements are used for the tangential variation in the sheet. However, the information about the discontinuity in normal direction is incorporated into the basis functions of the volume elements that are connected to the sheet elements. The determination of the normal variation can be reduced to a 1D problem which can be solved analytically. No double layers or global asymptotic expansions are required. The advantages with respect to the condition number of the system matrix are shown for a magneto-quasistatic test scenario.