Accurate Discretisation of a Nonlinear Micromagnetic Problem
| Author(s) | Monk, Peter B. | |
| Author(s) | Vacus, O. | |
| Date Accessioned | 2005-02-18T18:33:09Z | |
| Date Available | 2005-02-18T18:33:09Z | |
| Publication Date | 2000 | |
| 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. | en |
| Sponsor | This work was partially supported by the Air FOrce Office of Scientific Research, Materials Command, USAF, grant F49620–98–1–0019. The U.S. Government retains a non-exclusive, royalty free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. Copyright is owned by SIAM to the extent not limited by these rights. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force of Scientific Research or the U.S. Government. | en |
| Extent | 692469 bytes | |
| MIME type | application/pdf | |
| URL | http://udspace.udel.edu/handle/19716/367 | |
| Language | en_US | |
| Publisher | Department of Mathematical Sciences | en |
| Part of Series | Technical Report: 2000-15 | |
| Title | Accurate Discretisation of a Nonlinear Micromagnetic Problem | en |
| Type | Technical Report | en |