Finite element modeling of unbounded problems using transformations: a rigorous, powerful and easy solution

Brunotte, X.; Meunier, G.; Imhoff, J.F.

doi:10.1109/20.124021

Cited by 96 publications

(52 citation statements)

References 12 publications

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“…The magnetic 0018-9464/$26.00 © 2011 IEEE field is the sum of two terms: The inductor field and the demagnetization field due to the magnetic reaction of the material (1) In general, inductor field is very low in our application (order of magnitude of the Earth's magnetic field), so a linear magnetic behavior law is suitable to properly model the phenomenon. We have (2) where is the constant, reduced, reversible and linear magnetic permeability of the material.…”

Section: Integral Volume Equation Formulationmentioning

confidence: 99%

“…Until now, the most used numerical method was the finite element method. Many papers have already been published about the computation of the magnetization [1], [2] and the coils effects [3].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, domain truncation with boundary conditions can lead to inaccuracies. To solve this problem, some efficient numerical tools have been proposed like the "infinite box" for instance [1]. Another difficulty is the very high ratio between the length of the ship and the thickness of the hull which leads to an unacceptable number of elements if the hull is meshed in its volume.…”

Section: Introductionmentioning

confidence: 99%

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Ships Magnetic Anomaly Computation With Integral Equation and Fast Multipole Method

et al. 2011

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This paper presents a coupling between integral volume equation method (IVEM) and a fast multipole algorithm (FMM) in order to model ships magnetic anomaly. complex geometries of real vessels associated with dense meshes can be treated in order to compute the magnetic field created by induced magnetization of the hull and coils degaussing systems. Our algorithm has been validated with measurements made on a real submarine mock-up.

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Section: Integral Volume Equation Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ships Magnetic Anomaly Computation With Integral Equation and Fast Multipole Method

et al. 2011

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“…The boundary element method is accelerated using hierarchical matrices. For ease of porting the software to the GPU, we use a space transformation method [16] instead of the accelerated boundary element method for the treatment of the open boundary problem in the steepest descent solver. In the LLG solver we set the torque term to zero.…”

Section: Comparison With Llg Solvermentioning

confidence: 99%

LaBonte's method revisited: An effective steepest descent method for micromagnetic energy minimization

Exl¹,

Bance²,

Reichel³

et al. 2014

Journal of Applied Physics

112

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We present a steepest descent energy minimization scheme for micromagnetics. The method searches on a curve that lies on the sphere which keeps the magnitude of the magnetization vector constant. The step size is selected according to a modified Barzilai-Borwein method. Standard linear tetrahedral finite elements are used for space discretization. For the computation of static hysteresis loops the steepest descent minimizer is faster than a Landau-Lifshitz micromagnetic solver by more than a factor of two. The speed up on a graphic processor is 4.8 as compared to the fastest single-core CPU implementation.

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“…20 The resulting open-boundary problem can be treated by a parallelepipedic shell transformation, which transforms the infinite exterior space of the magnet on a shell around the magnet. 21 A brief description of the micromagnetic finite-element method used to discrete the magnets was reported in our previous works 3, [17][18][19] and more details can be found in the works by Schrefl et al 22 and Fisher et al 15,23 An isotropic single-phase magnet was constructed by assembling of 64 cubic Nd 2 Fe 14 B grains with random orientation, as shown in the inset of Fig. 1͑a͒.…”

mentioning

confidence: 99%

Grain boundary contribution to recoil loop openness of exchange-coupled nanocrystalline magnets

Rong

Liu

2009

Applied Physics Letters

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It has been well known that recoil loop openness is related to soft-phase presence in exchange-coupled hard-soft nanocomposite magnets. Our study on recoil loop openness of exchange-coupled nanocrystalline magnets ͑both single-phase and composite͒ using a micromagnetic finite-element method has revealed that the recoil loop openness is also due to decreased grain size. Open recoil loops exist in single-phase magnets as well. Simulation of magnetization distribution in both nanocrystalline single-phase magnets and nanocomposite magnets shows that the openness of the recoil loops is correlated with unstable magnetization behavior in grain boundary and soft-phase regions, which is attributed to high energy state caused by exchange coupling in these regions. The simulation results are supported by experimental data. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3127226͔Magnetically hard/soft exchange-coupled nanocomposites show enhanced magnetic properties due to intergrain exchange interactions. 1-3 Strength of the intergranular exchange coupling in these types of materials can be evaluated by measuring the remanence ratio or recoil loops. Analysis of recoil loops can provide deep physical insight into magnetization reversal behavior in nanocomposite magnets. [4][5][6][7][8][9][10][11][12][13] However, physical origin of the open recoil loops in nanocrystalline magnets is still not well understood. [11][12][13] It is commonly accepted that the open recoil loop phenomena were resulted from exchange decoupled soft phase in a nanocomposite magnet. [4][5][6][7][8][9][10] Recently, the recoil loop openness was found to be related to the inhomogeneity in the magnetic anisotropy, 11 unstable magnetic moments affected by thermal fluctuation, 12 and variations of exchange interactions in nanocomposite magnets. 13 It seems that the origin of open recoil loops in nanocrystalline magnets is more complex than what was previously thought and needs to be further studied.Micromagnetic simulation is an effective method to study magnetization behaviors inside nanostructured magnets since it gives a clear physics explanation on mechanisms of magnetization distribution and reversal. [14][15][16][17][18][19] In this work, we extend our study from nanocomposite magnets to singlephase magnets as well, to investigate the origin of recoil loop openness in exchange-coupled nanocrystalline magnets by using a micromagnetic finite-element method. It is revealed that not only the soft phases but also grain boundaries contribute to openness of the recoil loops.The equilibrium magnetization distribution under external magnetic field is calculated by the minimization of the total magnetic Gibbs free energy. It should be mentioned here that a magnetic vector potential was introduced to calculate the upper bound of the stray field energy, which was suggested by Brown. 20 The resulting open-boundary problem can be treated by a parallelepipedic shell transformation, which transforms the infinite exterior space of the magnet on a shell around t...

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Finite element modeling of unbounded problems using transformations: a rigorous, powerful and easy solution

Cited by 96 publications

References 12 publications

Ships Magnetic Anomaly Computation With Integral Equation and Fast Multipole Method

Ships Magnetic Anomaly Computation With Integral Equation and Fast Multipole Method

LaBonte's method revisited: An effective steepest descent method for micromagnetic energy minimization

Grain boundary contribution to recoil loop openness of exchange-coupled nanocrystalline magnets

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