Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics

Tools

Mauser, Norbert J. and Pfeiler, Carl-Martin and Praetorius, Dirk and Ruggeri, Michele (2022) Unconditional well-posedness and IMEX improvement of a family of predictor-corrector methods in micromagnetics. Applied Numerical Mathematics, 180. pp. 33-54. ISSN 0168-9274 (https://doi.org/10.1016/j.apnum.2022.05.008)

[thumbnail of Mauser-etal-ANM-2022-Unconditional-well-posedness-and-IMEX-improvement-of-a-family-of-predictor-corrector-methods]
Preview
 Text. Filename: Mauser_etal_ANM_2022_Unconditional_well_posedness_and_IMEX_improvement_of_a_family_of_predictor_corrector_methods.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo
Download (1MB)| Preview

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.

ORCID iDs

Mauser, Norbert J., Pfeiler, Carl-Martin, Praetorius, Dirk and Ruggeri, Michele ORCID logoORCID: https://orcid.org/0000-0001-6213-1602;
  • Item type:Article
    ID code:80813
    Dates:
    Date
    Event
    31 October 2022
    Published
    25 May 2022
    Published Online
    15 May 2022
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:19 May 2022 09:26
    Last modified:12 Dec 2024 17:30
    URI:https://strathprints.strath.ac.uk/id/eprint/80813
CORE (COnnecting REpositories)