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

François Alouges

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

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

Abstract

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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.

How to cite

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Alouges, 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

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  1. 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).  Zbl0479.65056
  2. W.F. Brown, Micromagnetics. Interscience Publishers, Wiley & Sons, New-York (1963).  
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  6. C.I. Goldstein, The finite element method with nonuniform mesh sizes for unbounded domains. J. Math. Comput.36 (1981) 387-404.  Zbl0467.65058
  7. J.D. Jackson, Classical Electrodynamics. Wiley and Sons, 2 nd edition (1975).  
  8. S.A. Nazarov and M. Specovius-Neugebauer, Approximation of exterior problems. Optimal conditions for the Laplacian. Analysis16 (1996) 305-324.  
  9. T. Shreffl, Numerische Simulation von Ummagnetisierungsvorgängen in hartmagnetischen Materialen, Ph.D. Thesis. Technische Universität Wien (1993).  
  10. 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.  
  11. 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).  
  12. L.A. Ying, Infinite Elements Method. Peking University Press.  

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