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

Authors:
Zhiping Li;Xiaonan Wu
Affiliations:
LMAM & School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, People's Republic of China
Venue:
Applied Numerical Mathematics
Year:
2004

Citing 4
Cited 1

Direct methods in the calculus of variations

Direct methods in the calculus of variations
A periodic relaxation method for computing microstructures

Applied Numerical Mathematics
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Grid generation and optimization based on centroidal Voronoi tessellations

Applied Mathematics and Computation

Non-conforming finite element and artificial boundary in multi-atomic Young measure approximation for micromagnetics

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

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.