# Mathematical and numerical studies of non linear ferromagnetic materials

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 3, page 593-626
- ISSN: 0764-583X

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topJoly, 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 -

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