Three-Dimensional Analysis of Magnetostatic Field by the Boundary Element Method Using Edge Elements

Abstract

Boundary element method is suitable for the three-dimensional analysis of magnetostatic field in the homogenous material without magnetic saturation. However, the requirement of the computer resources for the three-dimensional boundary element analysis becomes large because the cofficient matrix of the final simultaneous equations is dense. In this paper, the authors try to reduce the number of unknowns by the use of accurate and stable approximation of unknown vector variables for efficient computation. An edge element on which magnetic flux density is defined as a vector variable and its divergence is equal to zero is proposed. In this case, we can expect that the computational accuracy is improved by introducing the zero-divergence constraint of the tangential components of the magnetic flux density. On the element, the discretized values of the tangential components and normal component are defined at the middle points of the edges and the center of gravity, respectively. The applicability of the proposed method is investigated by the computation results of the magnetic sphere model and the benchmark model of the IEE of Japan for the three-dimensional magnetostatic problems.