What are different methods to solve the Landau Lifshitz Differential Equation?
Dear Colleague,
Good Day,
This is one method: 1- General solution of the Landau-Lifshitz-Gilbert equations linearized around a Bloch wall.
Phys. Rev. B 43, 5908 – Published 1 March 1991.
This is second method: 2- Accuracy of the Backward-Difference Solution of the Landau–Lifshitz–Gilbert Equation. Nobuo Hayashi et al 2003 Jpn. J. Appl. Phys. 42 1250. doi:10.1143/JJAP.42.1250, Received 10 September 2002, accepted for publication 14 November 2002. Published 1 March 2003.
This is a third method: 3- Numerical Methods for the Landau-Lifshitz-Gilbert Equation.
L’ubomír Baňas , Numerical Analysis and Its Applications
Lecture Notes in Computer Science Volume 3401, 2005, pp 158-165.
this is a 4th method: 4- Precession Axis Modification to a Semi-analytical Landau-Lifshitz Solution Technique.See ( the attached paper ' mmm07-ap21-final')
Please see, also, the attached article ( numerical) and an excellent Survey on the Numerics and Computations for the LL (surveyLL) .
Dear Vaibhavi,
Which Landau-Lifshitz equation are you interested in? There are a number of different possibilities. If you are interested in radiation reaction then let me know and I will post some suggestions for references.
Best regards,
David
Hi Vaibhavi,
Hazim's response on Landau-Lifshitz-Gilbert was very thorough, especially the survey he linked to, but it might be even too thorough? Depends on what you are looking for, of course. I just would like to add that "Gilbert" in the name of the equation refers to a dissipation term, and LL is the version with dissipation coefficient set to zero. More in my paper from 2004
BIT Volume 44, Issue 3, pp. 403-424
which has narrower scope than the survey but also has an algorithmic solution. The algorithm is quite a general principle of constructing composition of simpler algorithms. Hope you find it useful. Copyright issues prevent me from uploading it to RG, sorry.
Cheers
Teijo
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