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

Published online by Cambridge University Press:  15 August 2002

François Alouges
François Alouges*
Affiliation:
Laboratoire de Mathématiques, Université d'Orsay, 91405 Orsay Cedex, France; [email protected].
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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.

Keywords

Micromagneticsfinite element methodpreconditionningexterior problems.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 629 - 647
Copyright
© EDP Sciences, SMAI, 2001

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References

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).
Givoli, D., Non-reflecting boundary conditions. J. Comp. Phys. 94 (1991) 1-29. CrossRef
Goldstein, C.I., The finite element method with nonuniform mesh sizes for unbounded domains. J. Math. Comput. 36 (1981) 387-404. CrossRef
J.D. Jackson, Classical Electrodynamics. Wiley and Sons, $2^{\rm nd}$ edition (1975).
Nazarov, S.A. and Specovius-Neugebauer, M., Approximation of exterior problems. Optimal conditions for the Laplacian. Analysis 16 (1996) 305-324. CrossRefPubMed
T. Shreffl, Numerische Simulation von Ummagnetisierungsvorgängen in hartmagnetischen Materialen, Ph.D. Thesis. Technische Universität Wien (1993).
Fisher, R., Shreffl, T., Kronmüller, H. and Fidler, J., Phase distribution and computed magnetic properties of high-remanent composite magnets. J. Magnetism and Magnetic Materials 150 (1995) 329-344. CrossRef
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.