薄板涡流问题的有限元法

A New Finite Element Method of the Eddy Current Problem in Thin Conducting Plates

提出使用磁场强度Ｈ作状态变量计算薄导体板中多连域涡流分布的方法。借助于磁场强度Ｈ的微分，在薄导体板的均值面的边界上，电场强度Ｅ的切向分量被耦合进有限元方程，而电场强度Ｅ的法向为零的边界条件被强加。使用变带宽高斯消去法求解产生的带状稀疏不对称方程组。因为剖分区域仅为导体极，本方法的计算代价很低。在一个工业模型上，该方法被检验，计算结果与测量结果一致。

In this paper, the magnetic field H is used as a state variable for calculating 3D multiply connected eddy current distributions in thin conducting plates. On the boundary of the mean surface of the conductor plate, the tangential component of E is coupled into the finite element equation by means of the differential of H. The resulting sparse banded unsymmetric set of equations is solved by using the Gaussian elimination. For the divided region is only the conductor plate, the computation cost is lower. The method is tested and the computing result is coinside with the one measured.