Dual finite element formulations for lumped reluctances coupling

Dular, Patrick; Gyselinck, Johan; Henneron, Thomas; Piriou, F.

doi:10.1109/tmag.2005.844348

Cited by 24 publications

(35 citation statements)

References 4 publications

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“…To solve the previous problem, the magnetic scalar formulation can be used by defining a magnetic scalar potential Ω in the whole domain. The magnetomotive force is introduced by a scalar function α [6] and the magnetic field can be expressed such that, H = -grad Ω -ε grad α with Ω = cst on Γ H1 and Γ H2 and α = 1 on Γ H1 and α = 0 on Γ -Γ H1 (5) Combining (3) and (5) in relation (2), we obtain the magnetic scalar potential formulation of the problem. The weak form to be solved is then written,…”

Section: A Problematicmentioning

confidence: 99%

“…The couple (R n (x), S n (y)) is calculated regarding the previous couples (R i (x), S i (y)) with i∈[1,n-1]. The function Ω' (see (6)) can be written such that:…”

Section: A Separated Representationmentioning

confidence: 99%

“…Each couple (R n (x),S n (y)) is calculated by solving iteratively two equations determined from (6). First, we suppose that S n (y) is known.…”

Section: B Determination Of (R N (X)s N (Y))mentioning

confidence: 99%

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Nonlinear Proper Generalized Decomposition Method Applied to the Magnetic Simulation of a SMC Microstructure

Henneron

Bénabou²,

Clénet³

2012

IEEE Trans. Magn.

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Improvement of the magnetic performances of Soft Magnetic Composites (SMC) materials requires to link the microstructures to the macroscopic magnetic behavior law. This can be achieved with the FE method using the geometry reconstruction from images of the microstructure. Nevertheless, it can lead to large computational times. In that context, the Proper Generalized Decomposition (PGD), that is an approximation method originally developed in mechanics, and based on a finite sum of separable functions, can be of interest in our case. In this work, we propose to apply the PGD method to the SMC microstructure magnetic simulation. A non-linear magnetostatic problem with the scalar potential formulation is then solved.

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Section: A Problematicmentioning

confidence: 99%

“…The couple (R n (x), S n (y)) is calculated regarding the previous couples (R i (x), S i (y)) with i∈[1,n-1]. The function Ω' (see (6)) can be written such that:…”

Section: A Separated Representationmentioning

confidence: 99%

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Nonlinear Proper Generalized Decomposition Method Applied to the Magnetic Simulation of a SMC Microstructure

Henneron

Bénabou²,

Clénet³

2012

IEEE Trans. Magn.

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“…For a perfect conductor , BC (5a) leads to an essential BC on the primary unknown that can be expressed via the definition of a surface scalar potential (in general single valued, if no net magnetic flux flows in ) [7], i.e.,…”

Section: B Perfect Conductors Perturbed To Real Onesmentioning

confidence: 99%

“…The reference formulation is of the form (13) where the perfect conductors are extracted from and and are only involved through their boundaries (added to ) with (15) strongly defined in . The surface integral term is non-zero only for the function grad [from (15)], the value of which is then the total surface current flowing in (this can be demonstrated from the general procedure developed in [7]). It is zero for all the other local test functions (at the discrete level, for any edge not belonging to ).…”

Section: B Perfect Conductors Perturbed To Real Onesmentioning

confidence: 99%

Subdomain Perturbation Finite-Element Method for Skin and Proximity Effects

Dular

Sabariego²,

Krähenbühl³

2008

IEEE Trans. Magn.

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Skin and proximity effects are calculated in both active and passive conductors via a subproblem finite-element method based on a perturbation technique. A reference limit problem considering either perfectly electric or magnetic conductors is first solved. It gives the source for eddy-current perturbation subproblems in each conductor with its actual conductivity or permeability and its own mesh. These subproblems accurately determine the current density distributions and ensuing losses in conductors of any shape in both frequency and time domains, overcoming the limitations of the impedance boundary condition technique.Index Terms-Eddy currents, finite-element method (FEM), perturbation method, skin and proximity effects.

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