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Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics.
- Source :
-
Applied Numerical Mathematics . Oct2022, Vol. 180, p33-54. 22p. - Publication Year :
- 2022
-
Abstract
- Recently, Kim & Wilkening (Convergence of a mass-lumped finite element method for the Landau–Lifshitz equation, Quart. Appl. Math., 76, 383–405, 2018) proposed two novel predictor-corrector methods for the Landau–Lifshitz–Gilbert equation (LLG) in micromagnetics, which models the dynamics of the magnetization in ferromagnetic materials. Both integrators are based on the so-called Landau–Lifshitz form of LLG, use mass-lumped variational formulations discretized by first-order finite elements, and only require the solution of linear systems, despite the nonlinearity of LLG. The first(-order in time) method combines a linear update with an explicit projection of an intermediate approximation onto the unit sphere in order to fulfill the LLG-inherent unit-length constraint at the discrete level. In the second(-order in time) integrator, the projection step is replaced by a linear constraint-preserving variational formulation. In this paper, we extend the analysis of the integrators by proving unconditional well-posedness and by establishing a close connection of the methods with other approaches available in the literature. Moreover, the new analysis also provides a well-posed integrator for the Schrödinger map equation (which is the limit case of LLG for vanishing damping). Finally, we design an implicit-explicit strategy for the treatment of the lower-order field contributions, which significantly reduces the computational cost of the schemes, while preserving their theoretical properties. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01689274
- Volume :
- 180
- Database :
- Academic Search Index
- Journal :
- Applied Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 157352719
- Full Text :
- https://doi.org/10.1016/j.apnum.2022.05.008