In this work, we study the application of a hybrid mixed domain decomposition (HMDD) method for the rotor-stator coupling of a permanent magnet synchronous machine. For this, we derive a variational formulation on the electric machine inspired by hybridized discontinuous Galerkin methods using a mixed magnetostatics problem, an affine material law and boundary conditions respecting the symmetry of the motor. We are then able to locate the resulting finite element method within the HMDD framework presented in arXiv:2604.22543. This enables us naturally to transfer the well-posedness results and error estimates for the HMDD method to the finite element method considered in this work. Lastly, as a proof of concept, we consider an academic example and compare the resulting magnetic flux density and potential lines to their counterparts obtained by a well-established in-house code using iso-geometric analysis.

翻译：本文研究了一种用于永磁同步电机转子-定子耦合的混合混合区域分解（HMDD）方法。为此，我们基于混合化间断伽辽金方法，利用混合静磁学问题、仿射材料本构关系以及满足电机对称性的边界条件，推导了电机的变分公式。随后，我们能够将所得到的有限元方法置于arXiv:2604.22543中提出的HMDD框架内。这使我们能够自然地将HMDD方法的适定性结果和误差估计转移到本文所考虑的有限元方法中。最后，作为概念验证，我们考虑了一个学术算例，并将其产生的磁通密度和等势线与通过成熟的自研等几何分析代码得到的结果进行了比较。