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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 B=μ0μr(|H|)H,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 W1(R3),and for a finite-dimensional approximation.The theoretical results are illustrated by numerical examples,which capture the known physical phenomena.
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 B = μ0μr (| H |) H, ie, 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 W1 (R3), and for a finite-dimensional approximation. The theoretical results are illustrated by numerical examples, which capture the known physical phenomena.