Accurate discretization of a non-linear micromagnetic problem

✍ Scribed by P.B. Monk; O. Vacus

• Book ID: 104266802
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 397 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00176-1

✦ Synopsis

In this paper we propose a ®nite element discretization of the Maxwell±Landau±Lifchitz±Gilbert equations governing the electromagnetic ®eld in a ferromagnetic material. Our point of view is that it is desirable for the discrete problem to possess conservation properties similar to the continuous system. We ®rst prove the existence of a new class of Liapunov functions for the continuous problem, and then for a variational formulation of the continuous problem. We also show a special continuous dependence result. Then we propose a family of mass-lumped ®nite element schemes for the problem. For the resulting semi-discrete problem we show that magnetization is conserved and that semi-discrete Liapunov functions exist. Finally we show the results of some computations that show the behavior of the fully discrete Liapunov functions.