Speaker
Description
Permanent magnets, such as neodymium-iron-boron (NdFeB), play a crucial role in enhancing the efficiency of power conversion devices, including wind turbines, sensors, and electric motors, cf. [1]. Due to their enormous potential to address current technological and societal challenges, such as reducing CO2 emissions, they are the subject of intensive research. The primary goals include improving their performance, replacing critical materials, and reducing the energy required for their production. Numerical simulations, particularly the finite element method (FEM), provide a powerful tool to accelerate the advancement of these materials. However, accurately simulating magnetic materials requires some care, especially when discretizing the magnetic field H. In this work, different formulations for the description of the magnetic field are introduced and compared with each other. The focus remains on the application of Ampre’s law using a vector potential formulation. To ensure the uniqueness of the magnetic vector potential, a gauge condition is applied, i.e., the Coulomb gauge, cf. [2]. Since the magnetic field involves the function space H(curl), the tangential components must be continuous, while the normal components are generally discontinuous. This requirement cannot be met by conventional node-based Lagrange elements; instead, edge-based or Nédélec elements are typically used, cf. [3]. Both interpolations are presented and compared with each other.
References:
[1] O. Gutfleisch, M.A. Willard, E. Brück, C.H. Chen, S.G. Sankar and J. Ping Liu. Magnetic Materials and Devices for the 21st Century: Stronger, Lighter, and More Energy Efficient. Advanced Materials, 23: 821–842, 2011.
[2] E. Creusé, P. Dular and S. Nicaise. About the gauge conditions arising in Finite Element magnetostatic problems. Computers and Mathematics with Applications, 77:1563–1582, 2019.
[3] J.C. Nédélec. A new family of mixed finite elements in R3. Numerische Mathematik, 1(50):57–81, 1986.
