Mathematical and numerical studies of non linear ferromagnetic materials

Joly, Patrick, and Vacus, Olivier. "Mathematical and numerical studies of non linear ferromagnetic materials." ESAIM: Mathematical Modelling and Numerical Analysis 33.3 (2010): 593-626. <http://eudml.org/doc/197482>.

@article{Joly2010,
abstract = { In this paper we are interested in the numerical modeling of absorbing ferromagnetic materials obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves. In this work we consider the 1D problem. We first show that the corresponding Cauchy problem has a unique global solution. We then derive a numerical scheme based on an appropriate modification of Yee's scheme, that we show to preserve some important properties of the continuous model such as the conservation of the norm of the magnetization and the decay of the electromagnetic energy. Stability is proved under a suitable CFL condition. Some numerical results for the 1D model are presented. },
author = {Joly, Patrick, Vacus, Olivier},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Maxwell equations; Laundau-Lifchitz-Gilbert equation; Hille-Yosida theorem; FDTD.; nonlinear ferromagnetic materials; Maxwell equation; FDTD; Landau-Lifshitz-Gilbert equation},
language = {eng},
month = {3},
number = {3},
pages = {593-626},
publisher = {EDP Sciences},
title = {Mathematical and numerical studies of non linear ferromagnetic materials},
url = {http://eudml.org/doc/197482},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Joly, Patrick
AU - Vacus, Olivier
TI - Mathematical and numerical studies of non linear ferromagnetic materials
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 3
SP - 593
EP - 626
AB - In this paper we are interested in the numerical modeling of absorbing ferromagnetic materials obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves. In this work we consider the 1D problem. We first show that the corresponding Cauchy problem has a unique global solution. We then derive a numerical scheme based on an appropriate modification of Yee's scheme, that we show to preserve some important properties of the continuous model such as the conservation of the norm of the magnetization and the decay of the electromagnetic energy. Stability is proved under a suitable CFL condition. Some numerical results for the 1D model are presented.
LA - eng
KW - Maxwell equations; Laundau-Lifchitz-Gilbert equation; Hille-Yosida theorem; FDTD.; nonlinear ferromagnetic materials; Maxwell equation; FDTD; Landau-Lifshitz-Gilbert equation
UR - http://eudml.org/doc/197482
ER -