Abstract In this article, we investigate the equations of magnetostaties for a configuration where a ferromagnetic material occupies a bounded domain and is surrounded by vacuum. Furthermore, the ferromagnetic law tak...Abstract In this article, we investigate the equations of magnetostaties 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｜）Hi 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.展开更多
文摘Abstract In this article, we investigate the equations of magnetostaties 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｜）Hi 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.
