Multi-atomic young measure and artificial boundary in approximation of micromagnetics

Zhiping Li*, Xiaonan WU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Some micromagnetic phenomena can be modelled by a minimization problem of a nonconvex energy. A numerical method to compute the micromagnetic field, which gives rise to a finite dimensional unconstrained minimization problem, is given and analyzed. In our method, the Maxwell's equation defined on the whole space is solved by a finite element method using artificial boundary, and the highly oscillatory magnetization structure is approximated by an element-wise constant Young measure supported on a finite number of unknown points on the unit sphere. Numerical experiments on some uniaxial and cubic anisotropic energy densities show that the method is efficient.

Original languageEnglish
Pages (from-to)69-88
Number of pages20
JournalApplied Numerical Mathematics
Volume51
Issue number1
DOIs
Publication statusPublished - Oct 2004

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Artificial boundary
  • Finite element method
  • Micromagnetic
  • Microstructure
  • Nonconvex energy minimization
  • Unbounded domain
  • Young measure

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