Comparison of various methods for the modeling of thin magnetic plates

Abstract

Computation of the magnetic field in thin plates is particularly difficult because nodes on opposite sides of the plate are very close together and because the elements inside the plate are very flat. Three different methods, together with corresponding variations and combinations were used to compute the magnetic field in the plate: the boundary element method, the finite element method, and use of thin plate transmission conditions. With classical methods, the results are good for all cases, provided the computation of coefficients is sufficiently accurate. For very thin plates, a fine meshing is required to avoid failure of the computation. A new method that avoids those problems was designed. Since the vector potential varies very steeply across the plate, the idea is to replace the real plate by an equivalent double layer of current. The result is a special transmission condition, relating the values of the vector potential and of the tangential magnetic field on both sides of the plate. This condition does not depend on the kind of numerical method used and has been introduced in finite element and boundary element methods. Comparison with previous results shows that this highly economical method is both accurate and valid. This is the case even for very thin plates, where other methods fail, particularly if the meshing is too coarse.