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