Immersed isogeometric analysis with boundary conformal method for magnetostatics: challenges and remedies

  • Elbadry, Yusuf Thaer (Technical University of Darmstadt)
  • Guarino, Giuliano (Ecole Polytechnique Fédérale de Lausanne)
  • Antolín, Pablo (Ecole Polytechnique Fédérale de Lausanne)
  • Weeger, Oliver (Technical University of Darmstadt)

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Numerical simulation of complex geometries can be computationally expensive and time-consuming, particularly due to the extensive effort required for geometry preparation and mesh generation. This challenge is especially pronounced in the modeling of electric machines, where multiple materials and voids are modeled within the physical domain. Using classical finite element methods (FEM) or multi-patch isogeometric analysis (IGA), the construction of conformal meshes can result in a large number of elements or patches, in addition to the significant meshing effort involved. Immersed boundary methods offer an attractive alternative by enabling a higher degree of automation and alleviating the need for body-conformal meshing. In the context of magnetostatics, these methods rely on embedding non-dominant material bodies within the dominant material, which is represented on a background grid. In this work, we employ an immersed boundary–conformal approach [1, 2, 3], where different bodies and interfaces are immersed into a background mesh and surrounded by a conformal boundary layer, to address magnetostatic problems. Multiple 2D benchmark problems are solved to compare solutions obtained using conformal IGA, trimming-based approaches, non–conformal patch methods, and the immersed boundary–conformal method. The results demonstrate that the proposed approach is a promising and efficient alternative for solving magnetostatic problems without requiring body-conformal meshes.