Fast computation for large magnetostatic systems adapted for micromagnetism

SIAM Journal on Scientific Computing

Volumn 26, Issue 6, 2005, Pages 2160-2175

  Labbé, Stéphane ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Block Toeplitz matrices; Finite volume method; Magnetostatics; Maxwell equations

Indexed keywords

APPROXIMATION THEORY; FERROMAGNETIC MATERIALS; FINITE VOLUME METHOD; MAGNETIC FIELD EFFECTS; MAGNETOSTATICS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MAXWELL EQUATIONS;

BLOCK-TOEPLITZ MATRICES; DISCRETE OPERATORS; FINITE VOLUME APPROXIMATION; MAGNETOSTATIC FIELDS;

COMPUTATIONAL METHODS;

EID: 27844560874     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/030601053     Document Type: Article

References (20)

1. F. ALOUGES, Mémoire d'habilitation à diriger des recherches, Ph.D. thesis, Département de Mathématique, Université Paris-Sud, Paris, 1999.
2. C. BERNARDI AND Y. MADAY, Approximations spectrales de problèmes aux limites elliptiques, Math. Appl. 10, Springer-Verlag, Paris, 1992.
3. W. F. BROWN, Micromagnetics, Interscience Publishers, New York, 1963.
4. P. G. CIARLET, Introduction to Numerical Linear Algebra and Optimisation, Cambridge University Press, Cambridge, UK, 1989.
5. R. DAUTRAY AND J. L. LIONS, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 5, Springer-Verlag, Berlin, 1992.
6. F. ETHERIDGE AND L. GREENGARD, A new fast-multipole accelerated Poisson solver in two dimensions, SIAM J. Sci. Comput., 23 (2001), pp. 741-760.
7. R. EYMARD, T. GALLOUËT, AND R. HERBIN, Finite volume methods, in Handbook of Numerical Analysis 7, Ph. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam, 2000, pp. 715-1022.
8. M. J. FRIEDMAN, Mathematical study of the nonlinear singular integral magnetic field equation I, SIAM J. Appl. Math., 39 (1980), pp. 14-20.
9. R. W. HOCKNEY AND J. W. EASTWOOD, Computer Simulations Using Particles, McGraw-Hill, New York, 1988.
10. V. L. IVAKHNENKO AND E. E. TYRTYSHNIKOV, Application of 3D Volume Integral to Solution of Electromagnetic Wave Scattering Problems, Technical Report EM-RR 22/95, Elegant Mathematics, 1995.
11. R. I. JOSEPH AND E. SCHLÖMANN, Demagnetizing field in nonelipsoïdal bodies, J. Appl. Phys., 36 (1965), pp. 1579-1593.
12. T. KATO, Perturbation Theory for Linear Operators, Grundlehren Math. Wiss. Einzeld. 132, Springer-Verlag, Berlin, 1966.
13. S. LABBÉ, Simulation Numérique du Comportement Hyperfréquence des Matériaux Ferromagnétiques, Ph.D. thesis, Université Paris 13, Paris, 1998.
14. S. LABBÉ AND P. Y. BERTIN, Microwave polarisability of ferrite particles with non-uniform magnetization, J. Magnetism and Magnetic Materials, 206 (1999), pp. 93-105.
15. Y. NAKATAMI, Y. UESAKA, AND N. HAYASHI, Direct solution of the Landau-Lifshitz-Gilbert equation for micromagnetics, Japanese J. Appl. Phys., 28 (1989), pp. 2485-2507.
16. J. C. NÉDÉLEC, Notions sur les Techniques d'éléments Finis, Mathématiques et Applications, Ellipses, Paris, 1992.
17. J. PHILLIPS AND J. WHITE, A precorrected-FFT method for electrostatic analysis of complicated 3-d structures, IEEE Trans. Circuits and Systems, 16 (1997), pp. 1059-1073.
18. M. E. SCHABES AND H. N. BERTRAM, Magnetization processes in ferromagnetic cubes, J. Appl. Phys., 1 (1988), pp. 1347-1357.
19. G. STRANG, A proposal for Toeplitz matrix calculation, Stud. Appl. Math., 74 (1986), pp. 171-176.
20. A. VIALLIX, Simulation de la Structure de Parois dans un Matériaux Magnétique, Ph.D. thesis, Institut National Polytechnique de Grenoble, Grenoble, France, 1990.