A convergent finite element approximation for the quasi-static Maxwell–Landau–Lifshitz–Gilbert equations

Le, Kim-Ngan; Tran, Thanh

doi:10.1016/j.camwa.2013.08.009

Cited by 21 publications

(34 citation statements)

References 12 publications

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“…1 μ of the measured initial permeability (implying negligible skin effect) in the electromagnetic diffusion equation [1]. Given the regular antiparallel domain structure of these materials and the lack of dw activity at high frequencies, a simple model for the high-frequency magnetization process is envisaged, where the magnetization dynamics is described by coupled Maxwell and Landau-Lifshitz-Gilbert (LLG) equations [6]- [10]. This model, basically proposed in [5], is made to describe here the magnetostatic effects associated with the actual regular system of transverse bar-like domains.…”

Section: Introductionmentioning

confidence: 99%

Modeling High-Frequency Magnetic Losses in Transverse Anisotropy Amorphous Ribbons

et al. 2015

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The superior high-frequency magnetic behavior of transverse anisotropy amorphous ribbons can be qualitatively interpreted in terms of rotation dominated magnetization process and quantitatively predicted describing the spin dynamics by the Landau-Lifshitz-Gilbert (LLG) equation in association with the electromagnetic diffusion equation. The theory is applied to comprehensive measurements performed on Co-based alloys, tested as field-annealed tapewound rings from dc to 1 GHz with combination of fluxmetric and transmission line methods. The LLG equation is numerically solved considering the role of magnetostatic, exchange, anisotropy, eddy current, and applied fields. It accurately describes the high-frequency energy losses, ensuing from eddy currents, and spin damping. By further considering the low-frequency domain wall contribution, a full scenario for the broadband losses is achieved.

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Section: Introductionmentioning

confidence: 99%

Modeling High-Frequency Magnetic Losses in Transverse Anisotropy Amorphous Ribbons

et al. 2015

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“…The general framework (although without inertial effects, i.e., the case ζ = 0) was established in earlier papers by finite-difference/element methods; see, for instance, [7][8][9][10][11]. The following results concern systems coupling the LLG equation with the Maxwell system [4,[12][13][14][15][16]. In the case of magnetoelastic interactions, a finite-difference scheme is proposed and its stability discussed; see [17].…”

Section: Lemma 11 If M Is a Solution Of Problemmentioning

confidence: 96%

A finite-difference scheme for a model of magnetization dynamics with inertial effects

Moumni

Tilioua²

2015

J Eng Math

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We consider a mathematical model describing magnetization dynamics with inertial effects. The model consists of a modified form of the Landau-Lifshitz-Gilbert equation for the evolution of the magnetization vector in a rigid ferromagnet. The modification lies in the presence of an acceleration term describing inertia. A semi-implicit finite-difference scheme for the model is proposed, and a criterion of numerical stability is given. Some numerical experiments are conducted to show the performance of the scheme.

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“…In particular, we show how the finite element spaces and their bases are constructed. In another article we conducted a convergence analysis [9].…”

Section: C683mentioning

confidence: 99%

A finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations

Tran

2013

ANZIAMJ

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The quasi-static Maxwell-Landau-Lifshitz-Gilbert equations which describe the electromagnetic behaviour of a ferromagnetic material are highly nonlinear. Sophisticated numerical schemes are required to solve the equations, given their nonlinearity and the constraint that the solution stays on a sphere. We propose an implicit finite element solution to the problem. The resulting system of algebraic equations is linear which facilitates the solution process compared to nonlinear methods. We present numerical results to show the efficacy of the proposed method.

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A convergent finite element approximation for the quasi-static Maxwell–Landau–Lifshitz–Gilbert equations

Cited by 21 publications

References 12 publications

Modeling High-Frequency Magnetic Losses in Transverse Anisotropy Amorphous Ribbons

Modeling High-Frequency Magnetic Losses in Transverse Anisotropy Amorphous Ribbons

A finite-difference scheme for a model of magnetization dynamics with inertial effects

A finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations

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