The extrapolated explicit midpoint scheme for variable order and step size controlled integration of the Landau-Lifschitz-Gilbert equation

Author(s)
Lukas Exl, Norbert Mauser, Thomas Schrefl, Dieter Süss
Abstract

A practical and efficient scheme for the higher order integration of the Landau-Lifschitz-Gilbert (LLG) equation is presented. The method is based on extrapolation of the two-step explicit midpoint rule and incorporates adaptive time step and order selection. We make use of a piecewise time-linear stray field approximation to reduce the necessary work per time step. The approximation to the interpolated operator is embedded into the extrapolation process to keep in step with the hierarchic order structure of the scheme. We verify the approach by means of numerical experiments on a standardized NIST problem and compare with a higher order embedded Runge-Kutta formula. The efficiency of the presented approach increases when the stray field computation takes a larger portion of the costs for the effective field evaluation.

Organisation(s)
Department of Mathematics, Physics of Functional Materials
External organisation(s)
University for Continuing Education Krems
Journal
Journal of Computational Physics
Volume
346
Pages
14-24
No. of pages
11
ISSN
0021-9991
DOI
https://doi.org/10.1016/j.jcp.2017.06.005
Publication date
10-2017
Peer reviewed
Yes
Austrian Fields of Science 2012
101014 Numerical mathematics, 103017 Magnetism
Keywords
ASJC Scopus subject areas
Computational Mathematics, Physics and Astronomy(all), Applied Mathematics, Numerical Analysis, Computer Science Applications, Modelling and Simulation, Physics and Astronomy (miscellaneous)
Portal url
https://ucris.univie.ac.at/portal/en/publications/the-extrapolated-explicit-midpoint-scheme-for-variable-order-and-step-size-controlled-integration-of-the-landaulifschitzgilbert-equation(9d9cfb2a-4108-4a1f-b16d-5edfcf9351ab).html