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

Tetsuya Ishiwata; Kota Kumazaki

doi:10.3934/proc.2015.0644

Article Contents

2015, Volume 2015: 644-651. Doi: 10.3934/proc.2015.0644 open access

This issue Previous Article An iterative approach to $L^\infty$-boundedness in quasilinear Keller-Segel systems Next Article On global dynamics in a multi-dimensional discrete map

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

Tetsuya Ishiwata^1, and
Kota Kumazaki^2,

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: August 31, 2014

Revised: March 31, 2015

Published: October 2015

Abstract Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 65M06, 35K55; Secondary: 35Q60.

Citation:

Related Papers

Cited by

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.
[2]	Weinan E, Xiao-ping Wang, Numerical methods for the Landau-Lifshitz equation, SIAM J. NUMER. ANAL. Vol. 38 (2001), 1647-1665.
[3]	François Alouges, A new finite element scheme for Landau-Lifschitz equations, Discrete. Conti. Dyn. Syst Vol. 1 (2008), no.2, 187-196.
[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.
[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.
[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.
[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.