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Adaptive techniques for Landau-Lifshitz-Gilbert equation with magnetostriction. (English) Zbl 1137.78001

Summary: We propose a time-space adaptive method for micromagnetic problems with magnetostriction. The considered model consists of coupled Maxwell’s, Landau-Lifshitz-Gilbert (LLG) and elastodynamic equations. The time discretization of Maxwell’s equations and the elastodynamic equation is done by backward Euler method, the space discretization is based on Whitney edge elements and linear finite elements, respectively. The fully discrete LLG equation reduces to an ordinary differential equation, which is solved by an explicit method, that conserves the norm of the magnetization.

MSC:

78A25 Electromagnetic theory (general)
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
74B20 Nonlinear elasticity
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74F15 Electromagnetic effects in solid mechanics
82D40 Statistical mechanics of magnetic materials
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References:

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