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See detailComparison of Nonlinear Domain Decomposition Schemes for Coupled Electromechanical Problems
Halbach, Alexandre ULg; Dular, Patrick ULg; Geuzaine, Christophe ULg

in IEEE Transactions on Magnetics (2016), 52(3),

The aim of this paper is to compare several domain decomposition schemes for nonlinear, coupled electromechanical problems. Both staggered and monolithic electrostatic/elastic formulations are considered ... [more ▼]

The aim of this paper is to compare several domain decomposition schemes for nonlinear, coupled electromechanical problems. Both staggered and monolithic electrostatic/elastic formulations are considered for the multiphysics problem. The domain decomposition is applied either to a single multiphysics iteration, which corresponds to a linear problem, or to the full nonlinear multiphysics resolution. In the latter, the problem solved at each domain decomposition iteration is nonlinear. The influence of the elastic wave’s frequency and the electrostatic potential on the convergence rate and the computational cost of the algorithm is investigated on a 2-D model of a vibrating micromembrane array. [less ▲]

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See detailDesign Sensitivity Analysis for Shape Optimization of Nonlinear Magnetostatic Systems
Kuci, Erin ULg; Henrotte, François; Duysinx, Pierre ULg et al

in IEEE Transactions on Magnetics (2016), 52(3),

The paper discusses the sensitivity analysis for the shape optimization of a nonlinear magnetostatic system, evaluated both by direct and adjoint approaches. The calculations rely on the Lie derivative ... [more ▼]

The paper discusses the sensitivity analysis for the shape optimization of a nonlinear magnetostatic system, evaluated both by direct and adjoint approaches. The calculations rely on the Lie derivative concept of differential geometry where the flow is the velocity field associated with the modification of a geometrical parameter in the model. The resulting sensitivity formulas can be expressed naturally in a finite element setting through a volume integral in the layer of elements connected to the surface undergoing shape modification. The accuracy of the methodology is analyzed on a 2D model of an interior permanent magnet motor (IPM), and on a 3D model of a permanent magnet system. [less ▲]

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See detailComputation of Source for Non-Meshed Coils in a Reduced Domain with A–V Formulation
Ferrouillat, Pauline; Guérin, Christophe; Meunier, Gérard et al

in IEEE Transactions on Magnetics (2016), 52(3),

The discretized source magnetic vector potential Aj, projected from source field Hs with H(curl,Ω) semi-norm, is studied for non-meshed coils with magnetic vector potential A and electric scalar potential ... [more ▼]

The discretized source magnetic vector potential Aj, projected from source field Hs with H(curl,Ω) semi-norm, is studied for non-meshed coils with magnetic vector potential A and electric scalar potential V formulation. As a novelty, source potential Aj is computed in a reduced domain Ωred instead of the complete domain Ω. For domains with fixed and moving parts, potential Aj can be computed on each part, for each of the related current sources, with no need to ensure its continuity between these parts. [less ▲]

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See detailFinite-Element Homogenization of Laminated Iron Cores With Inclusion of Net Circulating Currents Due to Imperfect Insulation
Gyselinck, Johan; Dular, Patrick ULg; Krähenbühl, Laurent et al

in IEEE Transactions on Magnetics (2016), 52(3),

This paper deals with the time-domain homogenization of laminated cores in 2-D or 3-D finite-element (FE) models of electromagnetic devices, allowing for net circulating current in the laminations (e.g ... [more ▼]

This paper deals with the time-domain homogenization of laminated cores in 2-D or 3-D finite-element (FE) models of electromagnetic devices, allowing for net circulating current in the laminations (e.g., due to imperfect or damaged insulation). The homogenization is based on the expansion of the induction throughout the lamination thickness using a set of orthogonal polynomial basis functions (BFs), in conjunction with the magnetic vector potential formulation. These BFs allow for net flux, net current, and skin effect in the laminations; by choosing the number of BFs, one can compromise between accuracy and computational cost. The approach is validated through a linear 2-D test case with in-plane imposed and induced current density. A brute-force model, in which all laminations are finely meshed, produces the reference solution. The extension to nonlinear 3-D problems is expected to be straightforward. [less ▲]

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See detailProgressive Current Source Models in Magnetic Vector Potential Finite-Element Formulations
Dular, Patrick ULg; Kuo-Peng, Patrick; Ferreira da Luz, Mauricio V. et al

in IEEE Transactions on Magnetics (2016), 52(3),

Progressive refinements of the current sources in magnetic vector potential finite-element (FE) formulations are done with a subproblem method. The sources are first considered through magnetomotive force ... [more ▼]

Progressive refinements of the current sources in magnetic vector potential finite-element (FE) formulations are done with a subproblem method. The sources are first considered through magnetomotive force or Biot–Savart models up to their volume FE models, from statics to dynamics. A novel way to define the source fields is proposed to lighten the computational efforts, through the conversion of the common volume sources to surface sources, without the need for any preresolution. Accuracy improvements can then be obtained for local currents and fields, and global quantities, i.e., inductances, resistances, Joule losses, and forces. [less ▲]

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See detailModel refinements of transformers via a subproblem finite element method
Dular, Patrick ULg; Kuo-Peng, Patrick; Ferreira da Luz, Mauricio et al

in Proceedings of ISEF 2015 (2015, September)

A progressive modeling of transformers is performed via a subproblem finite element method. A complete problem is split into subproblems with different adapted overlapping meshes. Model refinements are ... [more ▼]

A progressive modeling of transformers is performed via a subproblem finite element method. A complete problem is split into subproblems with different adapted overlapping meshes. Model refinements are performed from ideal to real flux tubes, 1-D to 2-D to 3-D models, linear to nonlinear materials, perfect to real materials, single wire to volume conductor windings, and homogenized to fine models of cores and coils, with any coupling of these changes. The proposed unified procedure efficiently feeds each subproblem via interface conditions, which lightens mesh-to-mesh sources transfers, and quantifies the gain given by each refinement on both local fields and global quantities. [less ▲]

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See detailCorrection of homogenized lamination stacks via a subproblem finite element method
Dular, Patrick ULg; Ferreira da Luz, Mauricio; Kuo-Peng, Patrick et al

in COMPEL (2015), 34(5), 1553-1563

Purpose – The purpose of this paper is to develop a subproblem finite element method for progressive modeling of lamination stacks in magnetic cores, from homogenized solutions up to accurate eddy current ... [more ▼]

Purpose – The purpose of this paper is to develop a subproblem finite element method for progressive modeling of lamination stacks in magnetic cores, from homogenized solutions up to accurate eddy current distributions and losses. Design/methodology/approach – The homogenization of lamination stacks, subject to both longitudinal and transversal magnetic fluxes, is first performed and is followed by local correction subproblems in certain laminations separately, surrounded by their insulating layers and the remaining laminations kept homogenized. The sources for the local corrections are originally defined via interface conditions to allow the coupling between homogenized and non-homogenized portions. Findings – The errors proper to the homogenization model, which neglects fringing effects, can be locally corrected in some selected portions via local eddy current subproblems considering the actual geometries and properties of the related laminations. The fineness of the mesh can thus be concentrated in these portions, while keeping a coupling with the rest of the laminations kept homogenized. Research limitations/implications – The method has been tested on a 2D case having linear material properties. It is however directly applicable in 3D. Its extension to the time domain with non-linear properties will be done. Originality/value – The resulting subproblem method allows accurate and efficient calculations of eddy current losses in lamination stacks, which is generally unfeasible for real applications with a single problem approach. The accuracy and efficiency are obtained thanks to a proper refined mesh for each subproblem and the reuse of previous solutions to be locally corrected only acting in interface conditions. Corrections are progressively obtained up to accurate eddy current distributions in the laminations, allowing to improve the resulting global quantities: the Joule losses in the laminations, and the resistances and inductances of the surrounding windings. [less ▲]

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See detailDesign Sensitivity Analysis for Shape Optimization of Nonlinear Magnetostatic Systems
Kuci, Erin ULg; Duysinx, Pierre ULg; Dular, Patrick ULg et al

in Proceedings of COMPUMAG 2015 (2015, June)

In this paper, a direct and an adjoint analytic sensitivity analysis for a nonlinear magnetostatic system is obtained, in the context of shape optimization for any design function. The calculations are ... [more ▼]

In this paper, a direct and an adjoint analytic sensitivity analysis for a nonlinear magnetostatic system is obtained, in the context of shape optimization for any design function. The calculations are based on the material derivative concept of continuum mechanics. The resulting sensitivity formula can be expressed as either a volume integral or as a boundary integral along the interface where shape modification occurs. A method for the calculation of the design velocity field and mesh updating scheme is introduced as well. The accuracy of the methodology is analysed on an inductor system, suggesting that the volume integration technique should be preferred. All methods are freely available for further testing in the open source environment GetDP/Gmsh. [less ▲]

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See detailWide range progressive inductor models in magnetic vector potential finite element formulations
Dular, Patrick ULg; Kuo-Peng, Patrick; Ferreira da Luz, Mauricio et al

in Proceedings of NUMELEC 2015 (2015, June)

Wide range progressive refinements of the inductors in magnetic vector potential finite element formulations are done with a subproblem method. Their current sources are first considered via magnetomotive ... [more ▼]

Wide range progressive refinements of the inductors in magnetic vector potential finite element formulations are done with a subproblem method. Their current sources are first considered via magnetomotive force or Biot-Savart models up to their volume finite element models, from statics to dynamics. A novel way to define the associated source fields is proposed to lighten the computational efforts, via the conversion of the common volume sources to surface sources, with no need of any pre-resolution. Accuracy improvements are then efficiently obtained for local currents and fields, and global quantities, i.e. inductances, resistances, Joule losses and forces. [less ▲]

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See detailComparison of Nonlinear Domain Decomposition Schemes for Coupled Electromechanical Problems
Halbach, Alexandre ULg; Dular, Patrick ULg; Geuzaine, Christophe ULg

in Proceedings of COMPUMAG 2015 (2015, June)

The aim of this paper is to compare several domain decomposition schemes for nonlinear, coupled electromechanical problems. Both staggered and monolithic electrostatic/elastic formulations are combined ... [more ▼]

The aim of this paper is to compare several domain decomposition schemes for nonlinear, coupled electromechanical problems. Both staggered and monolithic electrostatic/elastic formulations are combined with an overlapping domain decomposition method applied either to the uncoupled, linear staggered resolutions or to the monolithic nonlinear system. The influence of the elastic waves frequency, of the electrostatic potential and of the mesh on the convergence rate is investigated on a simple 2D model of a vibrating micromembrane array. [less ▲]

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See detailComputation of Source for Non-Meshed Coils in a Reduced Domain with A–V Formulation
Ferrouillat, Pauline; Guérin, Christophe; Meunier, Gérard et al

in Proceedings of COMPUMAG 2015 (2015, June)

The discretized source magnetic vector potential Aj, interpolated from source field Hs with H(curl,Ω) semi-norm, is studied for non-meshed coils with magnetic vector potential A and electric scalar ... [more ▼]

The discretized source magnetic vector potential Aj, interpolated from source field Hs with H(curl,Ω) semi-norm, is studied for non-meshed coils with magnetic vector potential A and electric scalar potential V formulation. As a novelty, source potential Aj is computed in a reduced domain Ωred instead of the complete domain Ω. For domains with fixed and moving parts, potential Aj can be computed on each part, for each of the related current sources, with no need to ensure its continuity between these parts. [less ▲]

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See detailFinite element models for studying the capacitive behaviour of wound components
De Grève, Zacharie; Dular, Patrick ULg; Sabariego, Ruth V. et al

in Proceedings of COMPUMAG 2015 (2015, June)

Finite element models of increasing accuracy are proposed for the study of the capacitive behaviour of wound magnetic components. Simple models, which are based on the classical assumption of a decoupling ... [more ▼]

Finite element models of increasing accuracy are proposed for the study of the capacitive behaviour of wound magnetic components. Simple models, which are based on the classical assumption of a decoupling between electric and magnetic fields, are first described. Formulations which enable such a coupling are then presented. The models are tested on various coreless inductors, made of round conductors or copper sheets. The results are discussed and compared with experimental data measured with an impedance analyzer. [less ▲]

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See detailTime-domain finite-element homogenisation of laminated iron cores with net circulating currents
Gyselinck, Johan; Dular, Patrick ULg; Krähenbühl, Laurent et al

in Proceedings of COMPUMAG 2015 (2015, June)

This paper deals with the time-domain homogenization of laminated cores in 2D or 3D finite element (FE) models of electromagnetic devices, in particular allowing for net circulating current in the ... [more ▼]

This paper deals with the time-domain homogenization of laminated cores in 2D or 3D finite element (FE) models of electromagnetic devices, in particular allowing for net circulating current in the laminations (which may result from imperfect or damaged insulation). The homogenization is based on the decomposition of the variation of the induction in the lamination thickness by means of a orthogonal set of polynomial basis functions, in conjunction with the magnetic vector potential (MVP) formulation. The conventional even skin-effect basis functions are linked to net flux, whereas the odd ones are now added so as to allow for net current. The approach is validated through a simple linear 2D test case, although the extension to 3D nonlinear problems is straightforward. [less ▲]

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See detailEfficient Delta-Parametrization of 2D Surface-Impedance Solutions
Krähenbühl, Laurent; Dular, Patrick ULg; Péron, Victor et al

in Proceedings of COMPUMAG 2015 (2015, June)

Impedance boundary condition methods (IBCs) are among the most efficient methods for solving time-harmonic eddy-current problems with a small skin depth (delta). However for a wide range of frequencies ... [more ▼]

Impedance boundary condition methods (IBCs) are among the most efficient methods for solving time-harmonic eddy-current problems with a small skin depth (delta). However for a wide range of frequencies (or material conductivities) the standard approach is no more efficient, since it requires for each frequency (or conductivity) the computation of a finite element (FE) complex-valued problem. Moreover, the accuracy of IBC decreases dramatically for large delta. As an extension of our previous work, we propose here a more detailed method of parametrization in delta of the 2D small-delta eddy-currents problem. This numerically efficient method gives a very good precision for all the frequencies difficult to address, i.e. from the frequency corresponding to the last good solution obtainable by meshing the conductor up to infinity (perfect conductor solution). [less ▲]

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See detailSubproblem Methodology for Progressive Finite Element Modeling of Transformers
Dular, Patrick ULg

in Proceedings of COMPUMAG 2015 (2015, June)

Model refinements of transformers are performed via a subproblem finite element method. A complete problem is split into subproblems with overlapping meshes, to allow a progressive modeling from ideal to ... [more ▼]

Model refinements of transformers are performed via a subproblem finite element method. A complete problem is split into subproblems with overlapping meshes, to allow a progressive modeling from ideal to real flux tubes, 1-D to 2-D to 3-D models, linear to nonlinear materials, perfect to real materials, wired to volume inductors, and homogenized to fine models of cores and coils, with any coupling of these changes. Its solution is the sum of the subproblem solutions. The procedure simplifies both meshing and solving processes, and quantifies the gain given by each refinement on both local fields and global quantities. Efficient ways to chain the refinements are proposed and tested. [less ▲]

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See detailProgressive Current Source Models in Magnetic Vector Potential Finite Element Formulations
Dular, Patrick ULg; Kuo-Peng, Patrick; Ferreira da Luz, Mauricio et al

in Proceedings of COMPUMAG 2015 (2015, June)

Progressive refinements of the current sources in magnetic vector potential finite element formulations are done with a subproblem method. The sources are first considered via magnetomotive force or Biot ... [more ▼]

Progressive refinements of the current sources in magnetic vector potential finite element formulations are done with a subproblem method. The sources are first considered via magnetomotive force or Biot-Savart models up to their volume finite element models, from statics to dynamics. A novel way to define the source fields is proposed to lighten the computational efforts, via the conversion of the common volume sources to surface sources, with no need of any pre-resolution. Accuracy improvements are then efficiently ob-tained for local currents and fields, and global quantities, i.e. inductances, resistances, Joule losses and forces. [less ▲]

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See detailImpédances de surface en 2D : comparaison de méthodes de paramétrisation en δ
Krähenbühl, Laurent; Dular, Patrick ULg; Péron, Victor et al

in Proceedings of NUMELEC 2015 (2015, June)

Les méthodes d’impédance de surface sont parmi les plus efficaces pour résoudre les problèmes de courants de Foucault à faible profondeur de pénétration (δ) en régime harmonique linéaire ... [more ▼]

Les méthodes d’impédance de surface sont parmi les plus efficaces pour résoudre les problèmes de courants de Foucault à faible profondeur de pénétration (δ) en régime harmonique linéaire. Cependant l’effort de calcul devient considérable lorsqu’on s’intéresse à une large gamme de fréquences (ou de conductivités), car chacun des résultats correspond à la résolution d’un problème d’éléments finis en valeurs complexes ; de plus, l’erreur est en δ2 et augmente donc très vite avec δ. Nous avions précédemment montré qu’un développement limité permet des paramétrisations en δ des solutions, très précises pour toutes les valeurs de δ comprises entre la limite conducteur parfait (δ→0) et les premiers résultats accessibles par maillage de l’effet de peau (δ=δFE), avec un coût numérique équivalent à celui de 2 résolutions. Nous comparons ici la précision de deux des méthodes possibles pour construire un tel développement limité. [less ▲]

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See detailMéthodes de calcul des sources pour des bobines non-maillées avec la formulation éléments finis A − V
Ferrouillat, Pauline; Guérin, Christophe; Meunier, Gérard et al

in Proceedings of NUMELEC 2015 (2015, June)

Dans cet article, différents calculs du champ électromagnétique source sont décrits pour la formulation éléments finis A − V avec des bobines non-maillées. Ces différents calculs sont appliqués ... [more ▼]

Dans cet article, différents calculs du champ électromagnétique source sont décrits pour la formulation éléments finis A − V avec des bobines non-maillées. Ces différents calculs sont appliqués sur une machine asynchrone pour définir la meilleure approche. Cette source doit pouvoir ensuite être utilisée sur un domaine réduit fixe ou en mouvement. [less ▲]

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See detailUsing a vector Jiles-Atherton hysteresis model for isotropic magnetic materials with the FEM, Newton-Raphson method and relaxation procedure
Guérin, Christophe; Jacques, Kevin; Sabariego, Ruth V. et al

in Proceedings of NUMELEC 2015 (2015, June)

This paper deals with the use of a vector Jiles- Atherton hysteresis model included in 2D finite element modelling. The Newton-Raphson algorithm is used with a relaxtion procedure, which ensures the ... [more ▼]

This paper deals with the use of a vector Jiles- Atherton hysteresis model included in 2D finite element modelling. The Newton-Raphson algorithm is used with a relaxtion procedure, which ensures the convergence in most of the cases. We have simulated a T-shaped magnetic circuit with rotating fields and then a three-phase transformer model. [less ▲]

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