Linear secondorder IMEXtype integrator for the (eddy current) LandauLifshitzGilbert equation
Abstract
Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and [Praetorius et al. (Comput. Math. Appl., 2017)], we propose a numerical algorithm for the integration of the nonlinear and timedependent LandauLifshitzGilbert (LLG) equation which is unconditionally convergent, formally (almost) secondorder in time, and requires only the solution of one linear system per timestep. Only the exchange contribution is integrated implicitly in time, while the lowerorder contributions like the computationally expensive stray field are treated explicitly in time. Then, we extend the scheme to the coupled system of the LandauLifshitzGilbert equation with the eddy current approximation of Maxwell equations (ELLG). Unlike existing schemes for this system, the new integrator is unconditionally convergent, (almost) secondorder in time, and requires only the solution of two linear systems per timestep.
 Publication:

arXiv eprints
 Pub Date:
 November 2017
 DOI:
 10.48550/arXiv.1711.10715
 arXiv:
 arXiv:1711.10715
 Bibcode:
 2017arXiv171110715D
 Keywords:

 Mathematics  Numerical Analysis;
 Physics  Computational Physics
 EPrint:
 IMA Journal of Numerical Analysis, 40 (2020), 28022838