Abstract
In this article, we investigate the equations of magnetostatics for a configuration where a ferromagnetic material occupies a bounded domain and is surrounded by vacuum. Furthermore, the ferromagnetic law takes the form
i.e., the magnetizing field H and the magnetic induction B are collinear, but the relative permeability µr is allowed to depend on the modulus of H. We prove the well-posedness of the magnetostatic problem under suitable convexity assumptions, and the convergence of several iterative methods, both for the original problem set in the Beppo-Levi space W 1(ℝ3), and for a finite-dimensional approximation. The theoretical results are illustrated by numerical examples, which capture the known physical phenomena.
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Descloux, J., Flueck, M. & Rappaz, J. Modelling and mathematical results arising from ferromagnetic problems. Sci. China Math. 55, 1053–1067 (2012). https://doi.org/10.1007/s11425-011-4306-6
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DOI: https://doi.org/10.1007/s11425-011-4306-6