On the Application of Hybrid Mixed Domain Decomposition Methods to Permanent Magnet Synchronous Machines

2026-05-29

AI Summary

This study addresses the challenge of magnetostatic modeling and efficient solution of rotor–stator coupling in permanent magnet synchronous motors by systematically introducing, for the first time, the hybrid mixed domain decomposition (HMDD) method into this field. A finite element framework is developed based on a hybrid magnetostatic variational formulation, affine material constitutive relations, and symmetric boundary conditions. The proposed approach inherits the well-posedness and error estimation theory of HMDD, substantially extending its applicability to electromagnetic field simulation in electric machines. Numerical experiments demonstrate excellent agreement between the computed magnetic flux density and magnetic potential distributions and high-fidelity isogeometric analysis results, thereby validating the method’s accuracy and effectiveness.

Abstract

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.

Problem

• Permanent Magnet Synchronous Machine
• Rotor-Stator Coupling
• Domain Decomposition
• Magnetostatics
• Finite Element Method

Innovation

• hybrid mixed domain decomposition
• permanent magnet synchronous machine
• discontinuous Galerkin
• variational formulation
• rotor-stator coupling