On a decoupled linear FEM integrator for eddy-current-LLG

References

• Gilbert T. A Lagrangian formulation of the gyromagnetic equation of the magnetic field. Phys. Rev. 1955;100:1243–1255.
   Google Scholar
• Landau L, Lifschitz E. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Z. Sowjetunion. 1935;8:153–168.
   Google Scholar
• Hubert A, Schäfer R. Magnetic domains. The analysis of magnetic microstructures, Corr. 3rd printing. Heidelberg: Springer; 1998.
   Google Scholar
• Alouges F, Soyeur A. On global weak solutions for Landau-Lifshitz equations: existence and nonuniqueness. Nonlinear Anal. 1992;18:1071–1084.
   Web of Science ®Google Scholar
• Visintin A. On Landau-Lifshitz equations for ferromagnetism. Japan J. Appl. Math. 1985;2:69–84.
   Google Scholar
• Alouges F. A new finite element scheme for Landau-Lifshitz equations. Discrete Continuous Dyn. Syst. Ser. S. 2008;1:187–196.
   Google Scholar
• Alouges F, Kritsikis E, Toussaint J. A convergent finite element approximation for Landau-Lifshitz-Gilbert equation. Phys. B. 2012;407:1345–1349.
   Web of Science ®Google Scholar
• Baňas L’, Bartels S, Prohl A. A convergent implicit finite element discretization of the Maxwell-Landau-Lifshitz-Gilbert equation. SIAM J. Numer. Anal. 2008;46:1399–1422.
   Web of Science ®Google Scholar
• Baňas L, Page M, Praetorius D. A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equation. Forthcoming 2013. arXiv:1303.4009.
   Google Scholar
• Bartels S, Ko J, Prohl A. Numerical analysis of an explicit approximation scheme for the Landau-Lifshitz-Gilbert equation. Math. Comp. 2008;77:773–788.
   Web of Science ®Google Scholar
• Bartels S, Prohl A. Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation. SIAM J. Numer. Anal. 2006;44:1405–1419.
   Web of Science ®Google Scholar
• Cimrak I. A survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism. Arch. Comput. Meth. Eng. 2008;15:277–309.
   Web of Science ®Google Scholar
• d’Aquino M, Serpico C, Miano G. Geometrical integration of Landau-Lifshitz-Gilbert equation based on the mid-point rule. J. Comput. Phys. 2005;209:730–753.
   Web of Science ®Google Scholar
• García-Cervera CJ. Numerical micromagnetics: a review. Bol. Soc. Esp. Mat. Apl. SEMA. 2007;39:103–135.
   Google Scholar
• Kruzik M, Prohl A. Recent developments in the modeling, analysis, and numerics of ferromagnetism. SIAM Rev. 2006;48:439–483.
   Web of Science ®Google Scholar
• Prohl A. Computational micromagnetism. Advances in numerical mathematics. Stuttgart: B.G. Teubner; 2001.
   Google Scholar
• Kim-Ngan Le, Tran T. A convergent finite element approximation for the quasi-static Maxwell-Landau-Lifshitz-Gilbert equations. Comp. Math. Appl. 2013; 66: 1389–1402. arXiv:1212.3369v1.
   Web of Science ®Google Scholar
• Bruckner F, Suess D, Feischl M, Führer T, Goldenits P, Page M, Praetorius D. Multiscale modeling in micromagnetics: well-posedness and numerical integration. Math. Models Methods Appl. Sci. 2014; in print.
   Web of Science ®Google Scholar
• Page M. On dynamical micromagnetism [PhD thesis]. Wien: Institute for Analysis and Scientific Computing, Vienna University of Technology; 2013.
   Google Scholar
• Monk PB. Finite element methods for Maxwell’s equations. Oxford: Oxford University Press; 2003.
   Google Scholar
• Brenner S, Scott L. The mathematical theory of finite element methods. New York (NY): Springer; 2002.
   Google Scholar
• Goldenits P. Konvergente numerische integration der Landau-Lifshitz-Gilbert Gleichung [Convergent numerical integration of the Landau-Lifshitz-Gilbert equation] (in German) [PhD thesis]. Wien: Institute for Analysis and Scientific Computing, Vienna University of Technology; 2012.
   Google Scholar
• Goldenits P, Hrkac G, Mayr M, Praetorius D, Suess D. An effective integrator for the Landau-Lifshitz-Gilbert equation. In: Proceedings of Mathmod 2012 Conference; 2012; Wien.
   Google Scholar
• Goldenits P, Praetorius D, Suess D. Convergent geometric integrator for the Landau-Lifshitz-Gilbert equation in micromagnetics. Proc. Appl. Math. Mech. 2011;11:775–776.
   Google Scholar
• Bartels S. Stability and convergence of finite-element approximation schemes for harmonic maps. SIAM J. Numer. Anal. 2005;43:220–238.
   Web of Science ®Google Scholar
• μ Mag-Website of NIST-Institute. Available from: http://www.ctcms.nist.gov/~rdm/mumag.org.html.
   Google Scholar