Multiscale finite element methods for 2D/1D problems have been studied in this work to demonstrate their excellent ability to solve real-world problems. These methods are much more efficient than conventional 3D finite element methods and just as accurate. The 2D/1D multiscale finite element methods are based on a magnetic vector potential or a current vector potential. Known currents for excitation can be replaced by the Biot-Savart-field. Boundary conditions allow to integrate planes of symmetry. All presented approaches consider eddy currents, an insulation layer and preserve the edge effect. A segment of a fictitious electrical machine has been studied to demonstrate all above options, the accuracy and the low computational costs of the 2D/1D multiscale finite element methods.

翻译：本文研究了适用于二维/一维问题的多尺度有限元方法，旨在展示其在解决实际问题中的卓越能力。这些方法比传统三维有限元方法效率更高，同时保持同等精度。二维/一维多尺度有限元方法基于磁矢量势或电流矢量势构建，其中已知的励磁电流可由毕奥-萨伐尔场替代。边界条件允许集成对称平面。所有提出的方法均考虑了涡流、绝缘层并保留了边缘效应。通过研究虚构电机的一段实例，验证了上述所有特性、精度以及二维/一维多尺度有限元方法的低计算成本。