Modelling a permanent magnet synchronous motor in FEniCSx for parallel high-performance simulations

James McDonagh, Nunzio Palumbo, Neeraj Cherukunnath, Nikolay Dimov, Nada Yousif

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There are concerns that the extreme requirements of heavy-duty vehicles and aviation will see them left behind in the electrification of the transport sector, becoming the most significant emitters of greenhouse gases. Engineers extensively use the finite element method to analyse and improve the performance of electric machines, but new highly scalable methods with a linear (or near) time complexity are required to make extreme-scale models viable. This paper introduces a three-dimensional permanent magnet synchronous motor model using FEniCSx, a finite element platform tailored for efficient computing and data handling at scale. The model demonstrates comparable magnetic flux density distributions to a verification model built in Ansys Maxwell with a maximum deviation of 7% in the motor’s static regions. Solving the largest mesh, comprising over eight million cells, displayed a speedup of 198 at 512 processes. A preconditioned Krylov subspace method was used to solve the system, requiring 92% less memory than a direct solution. It is expected that advances built on this approach will allow system-level multiphysics simulations to become feasible within electric machine development. This capability could provide the near real-world accuracy needed to bring electric propulsion systems to large vehicles.
Original languageEnglish
Article number103755
Pages (from-to)1-14
Number of pages14
JournalFinite Elements in Analysis and Design
Early online date6 Apr 2022
Publication statusPublished - 1 Jul 2022


  • Electric machine
  • FEniCS
  • Finite element method
  • High-performance computing
  • Maxwell's equations
  • Open-source software


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