# American Institute of Mathematical Sciences

2015, 2015(special): 644-651. doi: 10.3934/proc.2015.0644

## Structure preserving finite difference scheme for the Landau-Lifshitz equation with applied magnetic field

 1 Mathematical Sciences, College of Systems Engineering and Science, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama 337-8570 2 Natural and Physical Sciences, Tomakomai National College of Technology, 443, Nishikioka, Tomakomai-shi, Hokkaido, 059-1275

Received  September 2014 Revised  April 2015 Published  November 2015

In this short paper we propose a finite difference scheme for the Landau-Lifshitz equation and an iteration procedure to solve the scheme. The key concept is structure-preserving''. We show that the proposed method inherits important mathematical structures from the original problem and also analysis the iteration.
Citation: Tetsuya Ishiwata, Kota Kumazaki. Structure preserving finite difference scheme for the Landau-Lifshitz equation with applied magnetic field. Conference Publications, 2015, 2015 (special) : 644-651. doi: 10.3934/proc.2015.0644
##### References:
 [1] Ivan Cimrák, A survey on the numerics and computations for the Landau-Lifschitz equation of micromagnetism, Arch. Comput. Methods. Eng Vol. 15 (2008), 277-309. Google Scholar [2] Weinan E, Xiao-ping Wang, Numerical methods for the Landau-Lifshitz equation, SIAM J. NUMER. ANAL. Vol. 38 (2001), 1647-1665. Google Scholar [3] François Alouges, A new finite element scheme for Landau-Lifschitz equations, Discrete. Conti. Dyn. Syst Vol. 1 (2008), no.2, 187-196. Google Scholar [4] A. Fuwa, T. Ishiwata and M. Tsutsumi, Finite difference schemes for Landau-Lifshitz equation, Proceedings of Czech-Japanese Seminar in Applied Mathematics 2006, COE Lecture Note, Kyushu University Vol. 6(2007), 107-113. Google Scholar [5] A. Fuwa, T. Ishiwata and M. Tsutsumi, Finite difference scheme for the Landau-Lifshitz equation, Japan J. Ind. Appl. Math. 29 (2012), 83-110. Google Scholar [6] Sören Bartels, Constraint preserving, Inexact solution of implicit discretizations of Landau-Lifshitz-Gilbert equations and consequences for convergence, PAMM proc.Appl. Math. Mech Vol. 6 (2006), 19-22. Google Scholar [7] Sören Bartels and Andreas Prohl, Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation, SIAM J. NUMER. ANAL. Vol. 44 (2006), pp.1405-1419. Google Scholar

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##### References:
 [1] Ivan Cimrák, A survey on the numerics and computations for the Landau-Lifschitz equation of micromagnetism, Arch. Comput. Methods. Eng Vol. 15 (2008), 277-309. Google Scholar [2] Weinan E, Xiao-ping Wang, Numerical methods for the Landau-Lifshitz equation, SIAM J. NUMER. ANAL. Vol. 38 (2001), 1647-1665. Google Scholar [3] François Alouges, A new finite element scheme for Landau-Lifschitz equations, Discrete. Conti. Dyn. Syst Vol. 1 (2008), no.2, 187-196. Google Scholar [4] A. Fuwa, T. Ishiwata and M. Tsutsumi, Finite difference schemes for Landau-Lifshitz equation, Proceedings of Czech-Japanese Seminar in Applied Mathematics 2006, COE Lecture Note, Kyushu University Vol. 6(2007), 107-113. Google Scholar [5] A. Fuwa, T. Ishiwata and M. Tsutsumi, Finite difference scheme for the Landau-Lifshitz equation, Japan J. Ind. Appl. Math. 29 (2012), 83-110. Google Scholar [6] Sören Bartels, Constraint preserving, Inexact solution of implicit discretizations of Landau-Lifshitz-Gilbert equations and consequences for convergence, PAMM proc.Appl. Math. Mech Vol. 6 (2006), 19-22. Google Scholar [7] Sören Bartels and Andreas Prohl, Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation, SIAM J. NUMER. ANAL. Vol. 44 (2006), pp.1405-1419. Google Scholar
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