Three-Dimensional Finite Element Eddy Current Analysis by Using High-Order Vector Elements

Abstract

Sets of high--order basis functions of a tetrahedral element are systematically constructed and applied to finite element analysis of eddy current problems. A polynomial space is divided into a lot of subspaces assigned on edges, faces and a volume of the tetrahedral element. Lagrange--type vector basis functions of the subspaces are presented. The effect of the high--order vector elements is investigated by a cubic conductor model located in ac steady--state magnetic fields. In the calculation by using the fundamental and second--order elements, no convergent value of the eddy current power loss can be obtained in spite of fine meshes because the eddy current shifts to the surface of the conductor. The higher--order vector elements give the convergent solutions in the coarse meshes.