Three-Dimensional Eddy Current Analysis by the Boundary Element Method Using Edge Elements

Abstract

Boundary element method is the one of the practical methods for three-dimensional eddy current analysis. The boundary element method using electric field and magnetic flux density as unknown variables was developed and its effectiveness has been shown. However, the large requirement of computer resources is a severe problem for the three-dimensional analysis. In this paper, a boundary element method using edge elements are proposed. The tangential components of unknown vector variable on the edge element are approximated by the linear vector function with respect to the area coordinates. On the edge element, the divergence of the linear vector function becomes zero and the rotation of the vector function becomes constant vector whose value is defined by the geometry of the edge element and the discretized values of the unknown vector variable. Using the vector function and the Maxwell's equations, the normal component of the electric field can be related to the tangential components of the magnetic flux density, and the normal component of the magnetic flux density can be related to the tangential components of the electric field. As a result of the relations, we can choose only the tangential components of the electric field and magnetic flux density as unknowns. Therefore, the number of unknowns is reduced remarkably, so that the computer resources for three-dimensional eddy current analysis may be reduced. In this paper, the formulation of the boundary element method using the edge elements is described and the applicability of the boundary element method is verified by numerical examples.