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See detailDesign sensitivity analysis for shape optimization based on the Lie derivative
Kuci, Erin ULg; Henrotte, François ULg; Duysinx, Pierre ULg et al

in Computer Methods in Applied Mechanics & Engineering (2017)

Abstract The paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations. The proposed approach, based on geometrical concepts borrowed ... [more ▼]

Abstract The paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations. The proposed approach, based on geometrical concepts borrowed from differential geometry, shows that sensitivity of a performance function (i.e. any function of the solution of the problem) with respect to a given design variable can be represented mathematically as a Lie derivative, i.e. the derivative of that performance function along a flow representing the continuous shape modification of the geometrical model induced by the variation of the considered design variable. Theoretical formulae to express sensitivity analytically are demonstrated in detail in the paper, and applied to a nonlinear magnetostatic and a linear elastic problem, following both the direct and the adjoint approaches. Following the analytical approach, one linear system of which only the right-hand side needs be evaluated (the system matrix being known already) has to be solved for each of the design variables in the direct approach, or for each performance functions in the adjoint approach. A substantial gain in computation time is obtained this way compared to a finite difference evaluation of sensitivity, which requires solving a second nonlinear system for each design variable. This is the main motivation of the analytical approach. There is some freedom in the definition of the auxiliary flow that represents the shape modification. We present a method that makes benefit of this freedom to express sensitivity locally as a volume integral over a single layer of finite elements connected to both sides of the surfaces undergoing shape modification. All sensitivity calculations are checked with a finite difference in order to validate the analytic approach. Convergence is analyzed in 2D and 3D, with first and second order finite elements. [less ▲]

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See detailUsing a Jiles‐Atherton vector hysteresis model for isotropic magnetic materials with the finite element method, Newton‐Raphson method, and relaxation procedure
Guérin, Christophe; Jacques, Kevin ULg; Vazquez Sabariego, Ruth et al

in International Journal of Numerical Modelling: Electronic Networks, Devices and Fields (2016)

This paper deals with the use of a Jiles‐Ather ton vector hysteresis model included in 2D finite element modeling. The hysteresis model is only valid for isotropic materials. It is implemented with the ... [more ▼]

This paper deals with the use of a Jiles‐Ather ton vector hysteresis model included in 2D finite element modeling. The hysteresis model is only valid for isotropic materials. It is implemented with the vector potential formulation in 2D along with electric circuit equations to account for a possible external circuit. The Newton‐Raphson algorithm is used with a relaxation procedure, whereby at each iteration, th e relaxation coefficient is sought so as to minimize the Euclidean norm of the residual of the finite element nonlinear system of equations. We have simulated several numerical examples with the proposed approach. First, simulation s on a square domain were conducted so as to validate the model. We have further simulated a T‐shaped magnetic circuit (exhibiting rotating flux) and a 3‐phase 3‐limb transformer model. For these 2 cases, the eddy current losses in the laminations are taken into account by a low‐frequency model. We have finally performed simulations on the TEAM workshop problem 32, which consists of a 3‐limb transformer with 2 windings, for which current and local magnetic flux density measurements are available. We obtained a good agreement between computed and measured results. [less ▲]

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See detailCo-simulation of Electromagnetic Transients and Phasor Models: a Relaxation Approach
Plumier, Frédéric ULg; Aristidou, Petros; Geuzaine, Christophe ULg et al

in IEEE Transactions on Power Delivery (2016), 31(5),

Co-simulation opens new opportunities to combine mature ElectroMagnetic Transients (EMT) and Phasor-Mode (PM) solvers, and take advantage of their respective high accuracy and execution speed. In this ... [more ▼]

Co-simulation opens new opportunities to combine mature ElectroMagnetic Transients (EMT) and Phasor-Mode (PM) solvers, and take advantage of their respective high accuracy and execution speed. In this paper, a relaxation approach is presented, iterating between an EMT and a PM solver. This entails interpolating over time the phasors of the PM simulation, extracting phasors from the time evolutions of the EMT simulation, and representing each sub-system by a proper multiport equivalent when simulating the other sub-system. Various equivalents are reviewed and compared in terms of convergence of the PM-EMT iterations. The paper also considers the update with frequency of the Thévenin impedances involved in the EMT simulation, the possibility to compute the EMT solution only once per time step, and the acceleration of convergence through a prediction over time of the boundary variables. Results are presented on a 74-bus, 23-machine test system, split into one EMT and one PM sub-system with several interface buses. [less ▲]

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See detailNonlinear Interpolation on Manifold of Reduced Order Models in Magnetodynamic Problems
Paquay, Yannick ULg; Bruls, Olivier ULg; Geuzaine, Christophe ULg

in IEEE Transactions on Magnetics (2016), 52(3), 1-4

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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 detailReduced Order Model for Accounting for High Frequency Effects in Power Electronic Components
Paquay, Yannick ULg; Geuzaine, Christophe ULg; Hasan, Md. Rokibul et al

in IEEE Transactions on Magnetics (2016)

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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 detailDomain Decomposition Methods for Time-Harmonic Electromagnetic Waves with High Order Whitney Forms
Marsic, Nicolas ULg; Waltz, Caleb; Lee, Jin-Fa et al

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

Classically, domain decomposition methods (DDM) for time-harmonic electromagnetic wave propagation problems make use of the standard, low order, Nédélec basis functions. This paper analyzes the ... [more ▼]

Classically, domain decomposition methods (DDM) for time-harmonic electromagnetic wave propagation problems make use of the standard, low order, Nédélec basis functions. This paper analyzes the convergence rate of DDM when higher order finite elements are used for both volume and interface discretizations, in particular when different orders are used in the volume and on the interfaces. [less ▲]

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See detailGetDDM: an Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic Wave Problems
Thierry, Bertrand; Vion, Alexandre; Tournier, Simon et al

in Computer Physics Communications (2016), 203

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See detailGeometrical validity of curvilinear pyramidal finite elements
Johnen, Amaury ULg; Geuzaine, Christophe ULg

in Journal of Computational Physics (2015), 299

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See detailSequential decision-making approach for quadrangular mesh generation
Johnen, Amaury ULg; Ernst, Damien ULg; Geuzaine, Christophe ULg

in Engineering with Computers (2015), 31(4), 729-735

A new indirect quadrangular mesh generation algorithm which relies on sequential decision-making techniques to search for optimal triangle recombinations is presented. In contrast to the state-of-art ... [more ▼]

A new indirect quadrangular mesh generation algorithm which relies on sequential decision-making techniques to search for optimal triangle recombinations is presented. In contrast to the state-of-art Blossom-quad algorithm, this new algorithm is a good candidate for addressing the 3D problem of recombining tetrahedra into hexahedra. [less ▲]

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See detailProgressive inductor modeling via a finite element subproblem method
Dular, Patrick ULg; Krähenbühl, Laurent; Ferreira da Luz, Mauricio et al

in COMPEL (2015), 34(3), 851-863

Purpose – The purpose of this paper is to develop a subproblem method (SPM) for progressive modeling of inductors, with model refinements of both source conductors and magnetic cores. Design/methodology ... [more ▼]

Purpose – The purpose of this paper is to develop a subproblem method (SPM) for progressive modeling of inductors, with model refinements of both source conductors and magnetic cores. Design/methodology/approach – The modeling of inductors is split into a sequence of progressive finite element (FE) SPs. The source fields (SFs) generated by the source conductors alone are calculated at first via either the Biot-Savart (BS) law or FEs. With a novel general way to define the SFs via interface conditions (ICs), to lighten their evaluation process, the associated reaction fields for each added or modified region, mainly the magnetic cores, and in return for the source conductor regions themselves when massive, are then calculated with FE models. Changes of magnetic regions go from perfect magnetic properties up to volume linear and nonlinear properties, and from statics to dynamics. Findings – For any added or modified region, the novel proposed ICs to define the SFs appear of general usefulness, which opens the method to a wide range of model improvements. Originality/value – The resulting SPM allows efficient solving of parameterized analyses thanks to a proper mesh for each SP and the reuse of previous solutions to be locally corrected, in association with novel SF ICs that strongly lighten the quantity of BS evaluations. Significant corrections are progressively obtained for the fields, up to nonlinear magnetic core properties and skin and proximity effects in conductors, and for the related inductances and resistances. [less ▲]

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See detailEfficient finite element assembly of high order Whitney forms
Marsic, Nicolas ULg; Geuzaine, Christophe ULg

in IET Science, Measurement & Technology (2015), 9(2), 204-210

This study presents an efficient method for the finite element assembly of high order Whitney elements. The authors start by reviewing the classical assembly technique and by highlighting the most time ... [more ▼]

This study presents an efficient method for the finite element assembly of high order Whitney elements. The authors start by reviewing the classical assembly technique and by highlighting the most time consuming part. Then, they show how this classical approach can be reformulated into a computationally efficient matrix-matrix product. They also address the global orientation problem of the vector valued basis functions. They conclude by presenting numerical results for a three-dimensional wave propagation problem. [less ▲]

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See detailSubproblem Finite-Element Refinement of Inductors From Wire to Static and Dynamic Volume Models
Dular, Patrick ULg; Péron, Victor; Krähenbühl, Laurent et al

in IEEE Transactions on Magnetics (2015), 51(3),

Progressive refinements of inductors are done with a subproblem method, from their wire or filament representations with Biot–Savart models up to their volume finite-element models, from statics to ... [more ▼]

Progressive refinements of inductors are done with a subproblem method, from their wire or filament representations with Biot–Savart models up to their volume finite-element models, from statics to dynamics. The reaction fields of additional magnetic and/or conducting regions are also considered. Accuracy improvements are efficiently obtained for local fields and global quantities, i.e., inductances, resistances, Joule losses, and forces. [less ▲]

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See detailRefinement of Homogenized Magnetodynamic Models of Wound Inductors Using Finite-Element Subproblems
De Grève, Zacharie; Dular, Patrick ULg; Gyselinck, Johan ULg et al

in IEEE Transactions on Magnetics (2015), 51(3),

In this paper, a methodology for refining the large-scale solutions obtained by 2-D magnetodynamic homogenized models of high-frequency inductor windings is proposed, based on the subproblem finite ... [more ▼]

In this paper, a methodology for refining the large-scale solutions obtained by 2-D magnetodynamic homogenized models of high-frequency inductor windings is proposed, based on the subproblem finite-element method. Two approaches are developed, depending on the type of source terms, which are employed to compute the corrections (namely, volumic or surfacic). An analysis of the error committed by the homogenized model, on the local (current densities in the conductors) as well as the global (resistance of the winding) level, is conducted, and appropriate correction strategies are proposed. For instance, it is shown that correcting some conductors in the vicinity of the air gap of an inductor is sufficient to get an acceptable value for the resistance. [less ▲]

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See detailSubproblem Finite-Element Refinement of Homogenized Dielectric Layers in Wound Inductors for Accurate Local Stresses Computation
De Grève, Zacharie; Dular, Patrick ULg; Meunier, Gérard et al

in IEEE Transactions on Magnetics (2015), 51(3),

Recently, a homogenized model in 2-D electrostatics has been proposed in order to avoid the meshing of the thin dielectric layers surrounding the conductors of transformers. The model performs a smoothing ... [more ▼]

Recently, a homogenized model in 2-D electrostatics has been proposed in order to avoid the meshing of the thin dielectric layers surrounding the conductors of transformers. The model performs a smoothing of the physical fields, which leads to an incorrect estimation of the peak values of the electric field between the conductors. This issue is critical for a correct design of the transformer insulation. Therefore, in this paper, the subproblem finite-element method is employed, so as to refine the homogenized model on selected areas, and recover the small scale variations of the fields. [less ▲]

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See detailAnisotropic and feature sensitive triangular remeshing using normal lifting
Nivoliers, Vincent; Lévy, Bruno; Geuzaine, Christophe ULg

in Journal of Computational and Applied Mathematics (2015), 289

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See detailA quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations
El Bouajaji, Mohamed; Thierry, Bertrand; Antoine, Xavier et al

in Journal of Computational Physics (2015), 294

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See detailPragmatic two-step homogenisation technique for ferromagnetic laminated cores
Henrotte, François; Steentjes, Simon; Hameyer, Kay et al

in IET Science, Measurement Technology (2015), 9(2), 152-159

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See detailA finite-element reciprocity solution for EEG forward modeling with realistic individual head models
Ziegler, Erik ULg; Chellappa, Sarah Laxhmi ULg; Gaggioni, Giulia ULg et al

in NeuroImage (2014), 103

Highlights • Creates EEG forward models suitable for high-resolution source localization. • Automatic T1-based whole-head finite element meshing and leadfield computation. • Pipelines can incorporate ... [more ▼]

Highlights • Creates EEG forward models suitable for high-resolution source localization. • Automatic T1-based whole-head finite element meshing and leadfield computation. • Pipelines can incorporate conductivity tensors from diffusion-weighted images. • Open-source toolbox shared under a permissive software license. • Accuracy comparable to SimBio FEM and superior to OpenMEEG BEM solutions. [less ▲]

Detailed reference viewed: 132 (27 ULg)