Fulltext

Modelling and mathematical results arising from ferromagnetic problems

Descloux, Jean ; Flueck, Michel ; Rappaz, Jacques

In: Science China Mathematics, 2012, vol. 55, no. 5, p. 1053-1067

Aggiungi alla tua lista
    Titre
    • Modelling and mathematical results arising from ferromagnetic problems
    Auteur
    • Descloux, Jean. Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015, Lausanne, Switzerland
    • Flueck, Michel. Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015, Lausanne, Switzerland
    • Rappaz, Jacques. Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015, Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Inglese
    Publié dans
    • Science China Mathematics, 2012, vol. 55, no. 5, p. 1053-1067. SP Science China Press
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:310548
    Summary
    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 $$B = \mu _0 \mu _r \left( {\left| H \right|} \right)H,$$ 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 W 1(ℝ3), and for a finite-dimensional approximation. The theoretical results are illustrated by numerical examples, which capture the known physical phenomena