×

Improved error estimates for a Maxwell-Landau-Lifschitz system. (English) Zbl 1354.78005

Summary: We study Maxwell’s system coupled with the Landau-Lifshitz (LL) equation. We consider the nonlinear dissipative case with a neglected exchange field. For a recent numerical scheme conserving magnitude of the magnetization we derive new error estimates and establish a better rate of convergence. These theoretical results are demonstrated on a numerical example. For computations we use the software package ALBERT.

MSC:

78A10 Physical optics
78M25 Numerical methods in optics (MSC2010)
35Q61 Maxwell equations

Software:

ALBERT
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] L’. Baňas M. Slodička A numerical scheme for a Maxwell-Landau-Lifshitz-Gilbert system. Applied Mathematics and Computation. Accepted for publication.
[2] A. Bossavit Computational electromagnetism. Variational formulations, complementarity, edge elements , volume XVIII of Electromagnetism. (Academic Press, Orlando, FL., 1998).
[3] M. Cessenat Mathematical methods in electromagnetism. Linear theory and applications. Series on Advances in Mathematics for Applied Sciences. 41. (World Scientific Publishers, Singapore, 1996). · Zbl 0917.65099
[4] W. E X.-P. Wang Numerical methods for the Landau-Lifshitz equation. SIAM J. Numer. Anal. , 38(5):1647-1665 (2000). · Zbl 0988.65079 · doi:10.1137/S0036142999352199
[5] B. Guo F. Su Global weak solution for the Landau-Lifshitz-Maxwell equation in three space dimensions. J. Math. Anal. Appl. , 211(1):326-346 (1997). · Zbl 0877.35122 · doi:10.1006/jmaa.1997.5467
[6] Joly, Electromagnetic wave propagation in presence of a ferromagnetic material, ESAIM, Proc. 3, pp 85– (1998) · Zbl 0913.65119
[7] Joly, Global solutions to Maxwell equations in a ferromagnetic medium, Ann. Henri Poincaré, 1 (2) pp 307– (2000)
[8] Joly, Mathematical and numerical studies of nonlinear ferromagnetic materials, M2AN, 33 (3) pp 593– (1999) · Zbl 0960.78003 · doi:10.1051/m2an:1999154
[9] Monk, Error estimates for a numerical scheme for ferromagnetic problems, SIAM J. Numer. Anal. 36 (3) pp 696– (1998) · Zbl 0924.65113 · doi:10.1137/S0036142997324228
[10] A. Prohl Computational micromagnetism, volume XVI of Advances in numerical mathematics. (Teubner, Leipzig, 2001).
[11] Slodička, Numerical study of nonlinear ferromagnetic materials, Appl. Numer. Math. 46 (1) pp 95– (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.