In this article, an easily implementable method to reduce the CPU time for some 3-D finite-element method (FEM) problems is presented. A translational displacement between two parts on both sides of a planar air gap is considered with a change of coordinates in the air-gap region along the $z$ -axis. To achieve this, formulation and postprocessing are slightly adapted. The proposed method is applied to an academic problem and to an axial electric rotating machine. Results are compared with a usual method. Time savings, ease of implementation, and precision on results are really encouraging with a strong reduction in the CPU time, keeping a low relative deviation. The method could be easily applied to any configurations with the planar air gap as an axial motor.

中文翻译：

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减少平面气隙 3D FEM 非线性问题计算时间的简单方法

在本文中，提出了一种易于实现的方法，可减少某些 3-D 有限元方法 (FEM) 问题的 CPU 时间。平面气隙两侧的两个部分之间的平移位移被认为是气隙区域中沿 $z$ 轴的坐标变化。为了实现这一点，对公式和后处理稍作调整。所提出的方法应用于学术问题和轴向旋转电机。结果与常规方法进行比较。通过大幅减少 CPU 时间并保持较低的相对偏差，节省时间、易于实施和结果精确确实令人鼓舞。该方法可以很容易地应用于平面气隙作为轴向电机的任何配置。