Accurate Discretisation of a Nonlinear Micromagnetic Problem
Date
2000
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
In this paper we propose a finite element discretization of the Maxwell-Landau-Lifchitz-Gilbert equations
governing the electromagnetic field 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 first 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 finite 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.