# Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 6, page 629-647
- ISSN: 1292-8119

## Access Full Article

top## Abstract

top## How to cite

topAlouges, François. "Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 629-647. <http://eudml.org/doc/197348>.

@article{Alouges2010,

abstract = {
This paper is devoted to the practical computation of the
magnetic potential induced by a distribution of magnetization in
the theory of micromagnetics. The problem turns out to be a coupling of
an interior and an exterior problem. The aim of this work is to describe
a complete method that mixes the approaches of Ying [12] and Goldstein
[6] which consists in constructing a mesh for the exterior
domain composed of homothetic layers. It has the advantage of being well
suited for catching the decay of the solution at infinity and giving a
rigidity matrix that can be very efficiently stored. All aspects are
described here, from the practical construction of the mesh, the storage
of the matrix, the error estimation of the method, the boundary conditions
and a simple preconditionning technique. At the end of the
paper, a typical computation of a uniformly magnetized
ball is done and compared to the analytic solution. This method
gives a natural alternatives to boundary elements methods for 3D
computations.
},

author = {Alouges, François},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Micromagnetics; finite element method; preconditionning; exterior problems.; micromagnetics; exterior problems},

language = {eng},

month = {3},

pages = {629-647},

publisher = {EDP Sciences},

title = {Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method},

url = {http://eudml.org/doc/197348},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Alouges, François

TI - Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 6

SP - 629

EP - 647

AB -
This paper is devoted to the practical computation of the
magnetic potential induced by a distribution of magnetization in
the theory of micromagnetics. The problem turns out to be a coupling of
an interior and an exterior problem. The aim of this work is to describe
a complete method that mixes the approaches of Ying [12] and Goldstein
[6] which consists in constructing a mesh for the exterior
domain composed of homothetic layers. It has the advantage of being well
suited for catching the decay of the solution at infinity and giving a
rigidity matrix that can be very efficiently stored. All aspects are
described here, from the practical construction of the mesh, the storage
of the matrix, the error estimation of the method, the boundary conditions
and a simple preconditionning technique. At the end of the
paper, a typical computation of a uniformly magnetized
ball is done and compared to the analytic solution. This method
gives a natural alternatives to boundary elements methods for 3D
computations.

LA - eng

KW - Micromagnetics; finite element method; preconditionning; exterior problems.; micromagnetics; exterior problems

UR - http://eudml.org/doc/197348

ER -

## References

top- A. Bayliss, M. Gunzburger and E. Turkel, Boundary conditions for the numerical solution of elliptic equations in exterior domains. SIAM J. Appl. Math.42 (1982).
- W.F. Brown, Micromagnetics. Interscience Publishers, Wiley & Sons, New-York (1963).
- X. Brunotte, G. Meunier and J.-F. Imhoff, Finite element modeling of unbounded problems using transformations: A rigorous, powerful and easy solution. IEEE Trans. Mag. 28 (1992).
- R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 6. Masson, Paris (1988).
- D. Givoli, Non-reflecting boundary conditions. J. Comp. Phys.94 (1991) 1-29.
- C.I. Goldstein, The finite element method with nonuniform mesh sizes for unbounded domains. J. Math. Comput.36 (1981) 387-404.
- J.D. Jackson, Classical Electrodynamics. Wiley and Sons, ${2}^{\mathrm{nd}}$ edition (1975).
- S.A. Nazarov and M. Specovius-Neugebauer, Approximation of exterior problems. Optimal conditions for the Laplacian. Analysis16 (1996) 305-324.
- T. Shreffl, Numerische Simulation von Ummagnetisierungsvorgängen in hartmagnetischen Materialen, Ph.D. Thesis. Technische Universität Wien (1993).
- R. Fisher, T. Shreffl, H. Kronmüller and J. Fidler, Phase distribution and computed magnetic properties of high-remanent composite magnets. J. Magnetism and Magnetic Materials150 (1995) 329-344.
- P.P. Silvester, D.A. Lowther, C.J. Carpenter and E.A. Wyatt, Exterior finite elements for 2-dimensional field problems with open boundaries. Proc. IEE 124 (1977).
- L.A. Ying, Infinite Elements Method. Peking University Press.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.