These slides were presented at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

In electromagnetic computational modeling, accurately predicting complex physical phenomena is crucial for understanding their industrial applications. In solid-state manufacturing, techniques like Induction Heating (IH) are widely used, for instance, for preheating in forging processes and enhancing mechanical properties through heat treatment [1]. Similarly, Magnetic Pulse Forming (MPF) enables the precise fabrication of complex parts and facilitates welding dissimilar materials without mechanical contact [2]. For processes involving liquid states or liquid-to-solid transitions, Electromagnetic Stirring (EMS) plays an important role, especially in continuous metal casting applications [3]. The Finite Element Method (FEM) has become a powerful tool for simulating such industrial problems, as it accommodates complex geometries and the coupling of diverse physical phenomena. However, achieving high accuracy in FEM simulations often requires fine domain discretization, which can lead to substantial computational costs. To address this challenge, adaptive remeshing techniques have been developed to optimize mesh distribution while reducing computational effort. This study proposes a methodology for anisotropic adaptive mesh refinement tailored to electromagnetic problems, leveraging the physics underlying the phenomena. The process begins with the definition of an a posteriori error estimator, which identifies regions in the computational domain that require enhanced resolution [4]. Then, a metric tensor is calculated to capture the anisotropy inherent in the electromagnetic phenomena [5]. Using this information, an automatic remeshing procedure dynamically adjusts the mesh size and shape, refining areas where the physical effects are most significant. This methodology ensures that computational resources are concentrated on critical regions, leading to more efficient and accurate simulations. This approach significantly reduces computational costs and CPU time, thereby enabling enhanced simulation of the industrial applications. Examples demonstrating the performance of the method will be presented, including an industrial case featuring full immersion of the inductors. References [1] V. Rudnev, D. Loveless, and R. L. Cook, Handbook of Induction Heating. CRC Press, 2017. doi: 10.1201/9781315117485. [2] J. R. Alves Zapata, 'œMagnetic pulse forming processes: Computational modelling and experimental validation,' Université de recherche Paris Sciences et Lettres, 2016. [3] U. Müller and L. Bühler, 'œMagnetofluiddynamics in Channels and Containers,' in Magnetofluiddynamics in Channels and Containers, Springer Berlin Heidelberg, 2001, pp. 1'“7. doi: 10.1007/978-3-662-04405-6_1. [4] J. O. Garcia C, J. R. Alves Z, J. Barlier, and F. Bay, 'œA-Posteriori Error Estimator for Finite Element Simulation of Electromagnetic Material Processing,' IEEE Trans Magn, 2022, doi: 10.1109/TMAG.2022.3212597. [5] B. F. Garcia C. Jesus O., Alves Z. José R, Ripert Ugo, Barlier Julien, 'œAnisotropic Mesh Adaptation Based on Error Estimation for 3D Finite Element Simulation of Electromagnetic Material Processing,' IEEE Trans Magn, 2023,