A convergent implicit finite element discretization of the Maxwell-Landau-Lifshitz-Gilbert equation

Lubomir Banas, Sören Bartels, Andreas Prohl

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

We propose an implicit, fully discrete scheme for the numerical solution of the Maxwell-Landau-Lifshitz-Gilbert equation which is based on linear finite elements and satisfies a discrete sphere constraint as well as a discrete energy law. As numerical parameters tend to zero, solutions weakly accumulate at weak solutions of the Maxwell-Landau-Lifshitz-Gilbert equation. A practical linearization of the nonlinear scheme is proposed and shown to converge for certain scalings of numerical parameters. Computational studies are presented to indicate finite-time blowup behavior and to study combined electromagnetic phenomena in ferromagnets for benchmark problems. © 2008 Society for Industrial and Applied Mathematics.

Original languageEnglish
Pages (from-to)1399-1422
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number3
DOIs
Publication statusPublished - 2008

Keywords

  • Convergence
  • Ferromagnetism
  • Finite elements
  • Maxwell-Landau-Lifshitz-Gilbert equation

Fingerprint Dive into the research topics of 'A convergent implicit finite element discretization of the Maxwell-Landau-Lifshitz-Gilbert equation'. Together they form a unique fingerprint.

  • Cite this