Improvement of the smoothing method in the finite element analysis

The finite element method (FEM) and the boundary element method (BEM) are very useful for the numerical analysis of electromagnetic phenomena. Although the FEM suits the analysis of a complicated region which could include non-linear materials or eddy currents, the physical quantities such as the magnetic flux densities B are obtained discretely. Therefore we have to make fine meshes for accurate estimation of the electromagnetic force by the Maxwell stress method. On the other hand the BEM makes it possible to derive continuous physical quantities at inner points by using analytical expressions, not by relying numerical derivation as in case of the FEM. In this paper we first use the FEM for analyzing the electromagnetic fields of the concrete model in terms of the magnetic vector potential A and the electric scalar potental φ. Next we locate the temporary boundary enclosing the region where we desire the values of B, and apply the BEM (using the H method or the φ method) to this region in order to obtain B continuously. Then we can calculate the electromagnetic force accurately by the Maxwell stress method. To verify this approach, the numerical results obtained by the proposed method are compared with the theoretical values.