Fiche individuelle
Thomas HENNERON  
Titre  MCF  
Equipe  Outils et Méthodes Numériques  
Adresse  Université de LILLE Avenue Paul langevin 59655 VILLENEUVED'ASCQ  
Téléphone  +33 (0)3 62 26 82 24  
thomas.henneron@univlille.fr  
Site personnel  https://www.researchgate.net/profile/Thomas_Henneron  
Observation / Thématique de recherche  Développement de modèles numériques en électromagnétisme, méthode des éléments finis, projection de solutions entre maillages, réduction de modèles numériques  
Publications 
ACLI Revue internationale avec comité de lecture 

[1] Model order reduction techniques applied to magnetodynamic TΩformulation The International Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), 05/2020 MULLER Fabian, CRAMPEN Lucas, HENNERON Thomas, CLENET Stéphane, HAMEYER Kay 
[2] Determination of stress dependent magnetostriction from a macroscopic magnetomechanical model and experimental magnetization curves Journal of Magnetism and Magnetic Materials (JMMM), Vol. 500, 04/2020, URL, Abstract M'ZALI Nabil, MARTIN Floran, AYDIN Ugur, BELAHCEN Anouar, BENABOU Abdelkader, HENNERON Thomas 
In this paper, we propose a method to identify the magnetostrictive behavior of electrical steel sheet submitted to a mechanical loading. The technique relies on the use of a magnetomechanical model including the magnetostrictive phenomenon, namely the anhysteretic JilesAthertonSablik (JAS) model, and experimental macroscopic
stress dependent magnetization curves. The method is illustrated with measured magnetization curves of a nonoriented (NO) electrical steel sheet under different stresses. Furthermore, the influence of a biaxial mechanical
loading on the magnetostrictive behavior is analyzed with the help of an equivalent stress. 
[3] 3D Numerical Modelling of Clawpole Alternators with its Electrical Environment IEEE Transactions on Magnetics, Vol. 56, N°. 1, 02/2020, Abstract CARON Guillaume, HENNERON Thomas, PIRIOU Francis, FAVEROLLE Pierre, MIPO JeanClaude 
This paper describes a methodology for modelling a sixphase clawpole alternator with its electrical environment. Magnetic
nonlinearities, eddy currents and rectifiers are taken into account. To solve magnetodynamic problems, we use the modified magnetic vector potential formulation. The complex structure of the machine requires a 3D finite element analysis. To limit the mesh size, we introduced a refinement strategy based on the calculation of the time derivative of magnetic vector potential, solution of the magnetostatic case. In addition, we propose to reduce the transient state by improving the initial solution from the solution of a magnetostatic problem. These different numerical techniques reduce drastically the computational time and memory resources. To validate the proposed approach, some results are compared with experimental ones. 
[4] FiniteElement Modeling of Magnetic Properties Degradation Due to Plastic Deformation IEEE Transactions on Magnetics, Vol. 56, N°. 2, 02/2020, URL, Abstract M'ZALI Nabil, MARTIN Floran, SUNDARIA Ravi, HENNERON Thomas, BENABOU Abdelkader, BELAHCEN Anouar 
In this article, the anhysteretic Sablik model is identified from measurements and implemented in a finiteelement (FE) code.
The model takes into account the effect of the plastic deformation through the dislocation density, and thus, enables to account for the degradation of the magnetic properties. A new model for magnetostriction is proposed and implemented in the Sablik model. Experimental data are used to identify the parameters of both Sablik model and proposed magnetostriction. Furthermore, the mechanical punching process of an electrical steel sheet is simulated in view of evaluating the plastic strain distribution near the punched edge. Based on the Sablik model and the simulated plastic strain, FE simulations are carried out on a steel sheet and a cage induction machine. The effect of the punching process on the distribution of magneticflux density and the magnetization current is analyzed. 
[5] StructurePreserved Reduced Order Modeling for Frequency Domain Solution of the Darwin Model with a Gauged Potential Formulation IEEE Transactions on Magnetics, Vol. 56, N°. 1, pages. 14, 01/2020, URL, Abstract YAN Shuai, TANG Zuqi, HENNERON Thomas, REN Zhuoxiang 
In this work, the proper orthogonal decomposition (POD) is applied for parametric analysis in the gauged potential formulation of the Darwin model considering both capacitive and inductive effects. Due to the large contrast in material parameters, the resulted system matrix is illconditioned. Also, the condition number of the corresponding snapshot complex matrix is very huge. To improve the stability of the POD method, a structuredpreserving strategy is considered and implemented for different unknown potentials, namely the magnetic vector potential A, the electric scalar potential φ, and the Lagrange multiplier p. Besides, a greedy algorithm is proposed to select the snapshots adaptively. Two numerical examples, including a parallel plate capacitor and a modified RLC device structure, are provided to illustrate the capability of proposed POD in model order reduction in frequency domain solvers. 
[6] Proper Generalized Decomposition for Edge Elements in Magnetostatics with Adaptive Stopping Criterion IEEE Transactions on Magnetics, Vol. 56, N°. 1, pages. 14, 01/2020, URL, Abstract YAN Shuai, TANG Zuqi, HENNERON Thomas, REN Zhuoxiang 
The proper generalized decomposition (PGD) is ana priorimodel order reduction (MOR) method based on a variableseparatedexpression of the problem. Two iterative loops are needed in the PGD algorithm, namely the outer loop for enriching the reductionmodes progressively, and the inner loop for solving each mode by fixed point iterations. Setting the stopping criterion of these twoloops blindly can cause either the inaccuracy of the PGD or a waste of iterations. In this work, a special variableseparated PGDwith edge elements is proposed and implemented on a hexahedral mesh in magnetostatics. Also, an adaptive stopping criterion basedon dual formulations is applied to balance different error components, namely the discretization error, error for outer and innerloops of PGD. A numerical example is given to illustrate the proposed approach 
[7] Surrogate Model based on the POD combined with the RBF Interpolation of Nonlinear Magnetostatic FE model IEEE Transactions on Magnetics, Vol. 56, N°. 1, pages. 14, 01/2020 HENNERON Thomas, PIERQUIN Antoine, CLENET Stéphane 
[8] Error Estimators for Proper Generalized Decomposition in TimeDependent Electromagnetic Field Problems IEEE Transactions on Magnetics, Vol. 56, N°. 1, 01/2020 MULLER Fabian, HENNERON Thomas, CLENET Stéphane, HAMEYER Kay 
[9] Mesh Deformation based on Radial Basis Function Interpolation
applied to Low Frequency Electromagnetic Problem IEEE Transactions on Magnetics, 06/2019 HENNERON Thomas, PIERQUIN Antoine, CLENET Stéphane 
[10] Exploitation of Independent Stator and Rotor Geometrical Periodicities in Electrical Machines Using the Schur Complement International Journal of Applied Electromagnetics and Mechanics (IJAEM), 02/2019 AL EIT Moustafa, CLENET Stéphane, HENNERON Thomas, GUYOMARCH Frédéric 
[11] Stabilised reducedorder model of a nonlinear eddy current problem
by a GappyPOD approach IEEE Transactions on Magnetics, 12/2018 HASAN Rokibul, MONTIER Laurent, HENNERON Thomas, SABARIEGO Ruth 
[12] FiniteElement Model Reduction of SurfaceMounted Permanent Magnet Machines by Exploitation of Geometrical Periodicity IEEE Transactions on Magnetics, Vol. 54, N°. 9, 09/2018, Abstract AL EIT Moustafa, CLENET Stéphane, HENNERON Thomas 
This paper presents a methodology that allows taking advantage of the geometrical periodicity of electrical machines together with the modeling of rotor motion. It enables by means of the discrete Fourier transform (DFT) to reduce the largescale system obtained from the finiteelement model to several smaller independent subsystems, allowing a shortening of the computational time. Due to DFT properties, the computational time can be more reduced especially when we consider the interdependence of the spectral components under either balanced or unbalanced supply condition. In addition, a further reduction is possible in the case of balanced regimes where the distribution of the eventual numerical solution is governed by a limited number of prevailing harmonics. 
[13] Matrix Interpolation based Reduced Order Modelling of a Levitation device with Eddy Current effects IEEE Transactions on Magnetics, Vol. 54, N°. 6, 06/2018 HASAN Rokibul, MONTIER Laurent, HENNERON Thomas, SABARIEGO Ruth 
[14] PODBased ReducedOrder Model of an EddyCurrent Levitation Problem Scientific Computing in Electrical Engineering. Mathematics in Industry, Vol. 28, 04/2018 HASAN Rokibul, MONTIER Laurent, HENNERON Thomas, SABARIEGO Ruth 
[15] DataDriven Model Order Reduction for Magnetostatic Problem Coupled with Circuit Equations IEEE Transactions on Magnetics, Vol. 54, N°. 3, 03/2018 PIERQUIN Antoine, HENNERON Thomas, CLENET Stéphane 
[16] Proper Generalized Decomposition Applied on a Rotating Electrical Machine IEEE Transactions on Magnetics, 03/2018 MONTIER Laurent, HENNERON Thomas, CLENET Stéphane, GOURSAUD Benjamin 
[17] Application of the Proper Generalized Decomposition to Solve MagnetoElectric Problem IEEE Transactions on Magnetics, 03/2018 HENNERON Thomas, CLENET Stéphane 
[18] Orthogonal Interpolation Method for Order Reduction of a Synchronous Machine Model IEEE Transactions on Magnetics, Vol. 54, N°. 2, pages. 16, 02/2018 FARZAM FAR Mehrnaz, MARTIN Floran, BELAHCEN Anouar, MONTIER Laurent, HENNERON Thomas 
[19] Robust Model Order Reduction of an Electrical Machine at Startup through Reduction Error Estimation International Journal of Numerical Modelling, 09/2017 MONTIER Laurent, HENNERON Thomas, CLENET Stéphane, GOURSAUD Benjamin 
[20] Rotation movement based on the Spatial Fourier Interpolation Method (SFIM) IEEE Transactions on Magnetics, Vol. 53, N°. 6, 06/2017, Abstract MONTIER Laurent, CLENET Stéphane, HENNERON Thomas, GOURSAUD Benjamin 
In the field of computational electromagnetics, taking into account the rotation of a subdomain is required to simulate certain devices such as electrical machines. Several methods have been proposed in the literature, but they remain quite difficult to implement. In this paper, we propose a sliding surface method based on a spatial Fourier interpolation in order to take into account any rotation angle with a very simple numerical implementation. 
[21] Structure Preserving Model Reduction of Low Frequency Electromagnetic Problem based on POD and DEIM IEEE Transactions on Magnetics, Vol. 53, N°. 6, 06/2017, Abstract MONTIER Laurent, PIERQUIN Antoine, HENNERON Thomas, CLENET Stéphane 
The Proper Orthogonal Decomposition (POD) combined with the (Discrete) Empirical Interpolation Method (DEIM) can be used to reduce the computation time of the solution of a FE model. However, it can lead to numerical instabilities. To increase the robustness, the POD_DEIM model must be constructed by preserving the structure of the full FE model. In this article, the structure preserving is applied for different potential formulations used to solve electromagnetic problems. 
[22] Comparison of DEIM and BPIM to Speed up a PODbased Nonlinear Magnetostatic Model IEEE Transactions on Magnetics, Vol. 53, N°. 6, 06/2017, Abstract HENNERON Thomas, MONTIER Laurent, PIERQUIN Antoine, CLENET Stéphane 
Proper Orthogonal Decomposition (POD) has been successfully used to reduce the size of the equation system and the computation time of linear Finite Element (FE) problems. With a nonlinear behavior law, the POD is not so efficient due to the computation cost of nonlinear entries of the full FE model. Then, the POD approach must be combined with an interpolation method of nonlinear terms to obtain an efficient reduced model. An interpolation method consists on the computation of a small number of nonlinear entries and on the interpolation of other terms. Different methods have been presented to select the set of nonlinear entries to be calculated. Then, the (Discrete) Empirical Interpolation method ((D)EIM) and the Best Points Interpolation Method (BPIM) have been developed. In this article, we propose to compare two reduced models based on the POD(D)EIM and on the PODBPIM in the case of nonlinear magnetostatics coupled with electric equation. 
[23] Balanced Proper Orthogonal Decomposition Applied to Magnetoquasistatic Problems Through a Stabilization Methodology IEEE Transactions on Magnetics, 04/2017 MONTIER Laurent, HENNERON Thomas, GOURSAUD Benjamin, CLENET Stéphane 
[24] Waveform relaxationNewton method to determine steady state: application to threephase transformer The International Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), Vol. 36, N°. 3, pages. 729740, 03/2017, Abstract CARON Guillaume, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
To determine the steady state of an electromagnetic structure with the finite element method without calculation of the transient state. The proposed method permits to reduce the computation time if the transient state is important. In the case of coupling magnetic and electric circuit equations to obtain the steady state with periodic conditions, an approach can be to discretise the time with periodic conditions and to solve the equation system. Unfortunately, the computation time can be prohibitive. In this paper, the authors proposed to use the waveform relaxation method associated to Newton method to accelerate the convergence. The obtained results show that the proposed approach is efficient if the transient state is important. On the contrary, if the transient is very low it is preferable to use the classical approach namely the time stepping finite element method. The main limitation of the proposed approach is the necessity to evaluate or to know the time constant and consequently the duration of the transient state. Moreover the method requires some important memory resources. In the context of the use of the time stepping finite element method, one of the problems is the computation time which can be important to obtain the steady state. The proposed method permits avoidance of this difficulty and gives directly the steady state. The novelty is the proposal of the waveform relaxation Newton method to obtain directly the steady state in the case of the study of the three phases transformer 
[25] A method coupling modified vector potential A* and homogenization formulations to model short circuits in lamination stacks The European Physical Journal  Applied Physics (EPJ AP), Vol. 75, N°. 3, pages. 11, 08/2016, Abstract ZIANI Smail, HENNERON Thomas, PUIGDELLIVOL Oriol, LE MENACH Yvonnick 
In this paper a method in 2D frequency domain is presented to simulate a laminated iron core with a shortcircuit between several magnetic sheets. The approach consists in coupling homogenization methods and finite element method. The defect is modeled with A* modified vector potential formulation and the rest of the structure with a homogenization method. The coupled method is applied to a lamination stack containing a shortcircuit and compared to the reference, where the A* formulation is applied on the whole domain. Finally, a thermal modeling of lamination stack is presented to study the influence of an insulating defect. 
[26] ModelOrder Reduction of Magnetoharmonic Problems Based on POD. Application to Planar Magnetic Components The European Physical Journal  Applied Physics (EPJ AP), Vol. 74, N°. 1, pages. 10903, 04/2016, URL, Abstract TAYLOR Laurent, HENNERON Thomas, MARGUERON Xavier, LE MENACH Yvonnick, LE MOIGNE Philippe 
Predetermination of losses and inductance values in the design phase, is necessary for the development
of highperformance magnetic components for power electronics. Numerical modeling, based on
the Finite Element Method (FEM) can be used to determine the characteristics of a particular component
with a complex geometry in high frequency (HF). These models are very accurate but the computation
time required is high compared to analytical models. The Model Order Reduction (MOR) methods can
be applied to reduce the computation time while maintaining high accuracy. Nowadays, the Proper Orthogonal
Decomposition (POD) is the most popular of MOR approaches. This technique has been applied
to study problems in many elds of engineering. In this paper, the POD method is developed to solve
magnetoharmonic problems in order to study a planar magnetic inductor. 
[27] Multirate coupling of controlled rectifier and nonlinear finite element model based on Waveform Relaxation Method IEEE Transactions on Magnetics, Vol. 52, N°. 3, 03/2016 PIERQUIN Antoine, HENNERON Thomas, BRISSET Stéphane, CLENET Stéphane 
[28] Multidisciplinary optimization formulation for the optimization of multirate systems IEEE Transactions on Magnetics, Vol. 52, N°. 3, 03/2016 PIERQUIN Antoine, BRISSET Stéphane, HENNERON Thomas 
[29] Time periodicity condition of nonlinear magnetostatic problem coupled with electric circuit imposed by Waveform Relaxation Method IEEE Transactions on Magnetics, Vol. 52, N°. 3, 03/2016, URL, Abstract CARON Guillaume, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
In numerical computation, the finite element (FE) method associated with external electric circuits is often used to evaluate electromagnetic devices with voltage sources. To study the solution of the steady state, the computation time can be prohibitive due to a large transient state compared to the time step used to discretize the time domain. In this paper, a method based on Waveform Relaxation Method is developed in order to impose the steady state of the solution in the case of a nonlinear magnetostatic problem coupled with electric circuit equations. 
[30] Transient simulation of an electrical rotating machine achieved through model order reduction Advanced Modeling and Simulation in Engineering Sciences, Vol. 3, N°. 10, 03/2016, URL, Abstract MONTIER Laurent, HENNERON Thomas, CLENET Stéphane, GOURSAUD Benjamin 
Model order reduction (MOR) methods are more and more applied on many different fields of physics in order to reduce the number of unknowns and thus the computational time of largescale systems. However, their application is quite recent in the field of computational electromagnetics. In the case of electrical machine, the numerical model has to take into account the nonlinear behaviour of ferromagnetic materials, motion of the rotor, circuit equations and mechanical coupling. In this context, we propose to apply the proper orthogonal decomposition combined with the (Discrete) empirical interpolation method in order to reduce the computation time required to study the startup of an electrical machine until it reaches the steady state. An empirical offline/online approach based on electrical engineering is proposed in order to build an efficient reduced model accurate on the whole operating range. Finally, a 2D example of a synchronous machine is studied with a reduced model deduced from the proposed approach. 
[31] SpaceTime Field Projection: FiniteElement Analysis Coupled Between Different Meshes and Different TimeStep Settings IEEE Transactions on Magnetics, Vol. 52, N°. 3, 03/2016 WANG Zifu, HENNERON Thomas, HOFMANN Heath 
[32] Application of the PGD and DEIM to Solve a 3D NonLinear Magnetostatic Problem Coupled With the Circuit Equations IEEE Transactions on Magnetics, Vol. 52, N°. 3, 03/2016 HENNERON Thomas, CLENET Stéphane 
[33] Reduction of a FiniteElement Parametric Model Using Adaptive POD Methods—Application to Uncertainty Quantification IEEE Transactions on Magnetics, Vol. 52, N°. 3, 03/2016 CLENET Stéphane, HENNERON Thomas, IDA Nathan 
[34] Error Estimation for Model Order Reduction of Finite Element Parametric Problems IEEE Transactions on Magnetics, Vol. 52, N°. 8, pages. 110, 03/2016, URL CLENET Stéphane, HENNERON Thomas 
[35] Optimisation process to solve multirate system Przeglad Elektrotechniczny, Vol. 2015, N°. 6, pages. 5457, 06/2015, URL PIERQUIN Antoine, BRISSET Stéphane, HENNERON Thomas, CLENET Stéphane 
[36] Proper Generalized Decomposition Method Applied to Solve 3D MagnetoquasiStatic Field Problems Coupling With External Electric Circuits IEEE Transactions on Magnetics, Vol. 51, N°. 6, 06/2015 HENNERON Thomas, CLENET Stéphane 
[37] ModelOrder Reduction of MultipleInput NonLinear Systems Based on POD and DEI Methods IEEE Transactions on Magnetics, Vol. 51, N°. 3, 04/2015 HENNERON Thomas, CLENET Stéphane 
[38] Energetic MeshtoMesh Projection of Magnetic Fields With Respect to Nonlinear BH Curves IEEE Transactions on Magnetics, Vol. 51, N°. 3, 04/2015 WANG Zifu, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
[39] EndRegion Leakage Fluxes and Losses Analysis of Cage Induction Motors Using 3D FiniteElement Method IEEE Transactions on Magnetics, Vol. 51, N°. 3, 04/2015, URL, Abstract CHEAYTANI Jalal, BENABOU Abdelkader, TOUNZI Abdelmounaïm, DESSOUDE Maxime, CHEVALLIER Loïc, HENNERON Thomas 
The stray load losses (SLLs) in electrical machines represent a nonnegligible contribution of the total losses and a key point for an accurate evaluation of the energy efficiency of considered device. In this paper, one aspect of these SLLs, the endregion leakage fluxes and losses, is investigated and considered for the case of a highpower cage induction motor. The study is performed at locked rotor, noload, and rated load conditions using a 3D finiteelement modeling approach. The influence of the leakage flux on the endregion conductive parts of the motor is analyzed together with the eddy current loss calculation. Finally, the SLLs are calculated and compared with the experimental measurements based on the IEEE standard 112method B test. 
[40] Error estimation of a proper orthogonal decomposition reduced model of a permanent magnet synchronous machine IET Science, Measurement & Technology, 03/2015 HENNERON Thomas, CLENET Stéphane 
[41] Model Order Reduction of Magnetoquasistatic Problems Based on POD and Arnoldibased Krylov Methods
IEEE Transactions on Magnetics , Vol. 51, N°. 3, 03/2015 PIERQUIN Antoine, HENNERON Thomas, CLENET Stéphane, BRISSET Stéphane 
[42] Energetic Galerkin Projection of Electromagnetic Fields Between Different Meshes IEEE Transactions on Magnetics, Vol. 50, N°. 2, pages. 613616, 02/2014, URL, Abstract WANG Zifu, TANG Zuqi, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
Meshtomesh field transfer arises frequently in finite element computations. Typical applications may concern remeshing, multigrid methods, domain decomposition and multiphysics problems. For electromagnetic fields, one of the essential constraints in such transfers is to conserve energetic quantities such as the magnetic energy and the joule heating. Within the framework of Galerkin projection on overlapping domains, we introduce the definition of energetic norms for electromagnetic fields. The corresponding formulations we propose, provide energyconserving projection of electromagnetic fields between different meshes. 
[43] Model Order Reduction of NonLinear Magnetostatic Problems Based on POD and DEI Methods IEEE Transactions on Magnetics, 02/2014 HENNERON Thomas, CLENET Stéphane 
[44] Model order reduction applied to the numerical study of electrical
motor based on POD method taking into account rotation
movement International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 02/2014 HENNERON Thomas, CLENET Stéphane 
[45] Benefits of Waveform Relaxation Method and Output Space Mapping for the Optimization of Multirate Systems IEEE Transactions on Magnetics, Vol. 50, N°. 2, pages. 653656, 02/2014, Abstract PIERQUIN Antoine, BRISSET Stéphane, HENNERON Thomas, CLENET Stéphane 
We present an optimization problem that requires the modeling of a multirate system composed of subsystems with different time constants. We use waveform relaxation method (WRM) in order to simulate such a system, but computation time can be penalizing in an optimization context. Thus, we apply output space mapping (OSM) that uses several models of the system to accelerate optimization. WRM is one of the models used in OSM. 
[46] Comparison of Implementation Techniques for Galerkin Projection Between Different Meshes Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 12/2013, Abstract WANG Zifu, HENNERON Thomas, DULAR Patrick, MIPO JeanClaude, PIRIOU Francis 
To solve multiphysics problems, weak coupling of finite element calculations can be carried out: the subproblems of which the physical nature differs, are solved separately on their own meshes.
In this case, Galerkin projection provides useful tool to ensure the transfer of physical fields between different meshes.
In terms of implementation, the Galerkin projection system can be either accurately assembled over the intersection of two meshes or approximately integrated over the target mesh.
This paper describes and compares these two implementation techniques for the Galerkin projection. 
[47] Model order reduction of quasistatic problems based on POD and PGD
approaches EPJ AP, Vol. 64, N°. 2, 10/2013 HENNERON Thomas, CLENET Stéphane 
[48] Electromagnetic Field Projection on Finite Element Overlapping Domains IEEE Transactions on Magnetics, Vol. 49, N°. 4, pages. 12901298, 04/2013, Abstract WANG Zifu, HENNERON Thomas, NEMITZ Nicolas, MIPO JeanClaude, PIRIOU Francis 
Coupled problems are made up of subproblems of which the physical
nature differs. Using indirect coupling models, the subproblems are calculated
separately on their own meshes to ensure precision. To
obtain a precise solution for the total problem, it is important to ensure the
transmission of information between the subproblems. In this
paper, we present field projection methods on overlapping domains.
In comparison to earlier works, the classical $L^{2}$ or $mathbf{L}^{2}$
projection theory is extended to $H(mathbf{grad})$, $mathbf{H}(mathbf{curl})$
and $mathbf{H}(div)$ to obtain increased projection accuracy for the distributional
derivatives. A PetrovGalerkin method is then presented to fill the
test space using a biorthogonal basis, without losing the optimality
of the result in comparison to the $L^{2}$ or $mathbf{L}^{2}$ RitzGalerkin
method. Using the PetrovGalerkin method and biorthogonal test functions,
the projection is presented using a diagonal matrix. However, in the
standard RitzGalerkin projections, a linear system must be solved. 
[49] Nonlinear Proper Generalized Decomposition Method Applied to the Magnetic Simulation of a SMC Microstructure IEEE Transactions on Magnetics, Vol. 48, N°. 11, 11/2012 HENNERON Thomas, BENABOU Abdelkader, CLENET Stéphane 
[50] Interlaminar short circuit detection: modeling and measurement Compel, Vol. 31, N°. 5, 08/2012, Abstract MÜLLER JulianaLuisa, ROMARY Raphaël, BENABOU Abdelkader, HENNERON Thomas, PIRIOU Francis, BASTOS João Pedro Assumpção, ROGER JeanYves 
Short circuits in turbogenerator stators can lead to a modification of the magnetic flux distribution that impacts the performances and, in some extreme cases, can lead to local damage of the iron core. This work presents the modeling of short circuited laminations in a stator yoke of a turbogenerator. A 3D finite element (FE) model, associated to a homogenization technique, is used to calculate the short circuit current. The results are compared with the experiment, especially for the electrical signature of the diagnosis test known as Electromagnetic Core imperfection detector (El Cid). 
[51] Mortar method using biorthogonal nodal functions applied to
Aphi formulation
IEEE transaction on magnetics, Vol. 48, N°. 2, 02/2012 AUBERTIN Mathieu, HENNERON Thomas, PIRIOU Francis 
[52] High Order Surface Impedance Boundary Conditions with the AΦ Formulation Facta Universitatis: Electronics and Energetics, Vol. 24, N°. 2, pages. 147155, 08/2011 IDA Nathan, LE MENACH Yvonnick, HENNERON Thomas 
[53] An approach to determine the circulation of magnetic field in FEM computation code with vector potential formulation IEEE transaction on magnetics, 01/2011 HENNERON Thomas, PIRIOU Francis, ROGER JeanYves 
[54] Overlapping finite elements used to connect nonconforming meshes in 3D with a vector potential formulation IEEE transaction on magnetics, 01/2011, Abstract KREBS Guillaume, HENNERON Thomas, CLENET Stéphane, LE BIHAN Yann 
Overlapping elements can be used to connect nonconforming meshes in the finiteelement method. This approach has been developed with the scalar potential formulation and used to solve magnetostatic problems but not in the case of the vector potential formulation. In this paper, we propose to introduce the overlapping element method in this second formulation 
[55] Periodic and Antiperiodic boundary conditions with the Lagrange multipliers in the FEM IEEE Transactions on Magnetics, Vol. 46, N°. 8, 08/2010, Abstract AUBERTIN Mathieu, HENNERON Thomas, PIRIOU Francis, GUERIN Pierre, MIPO JeanClaude 
An approach based on the double Lagrange multipliers is developed in the finite element method in order to impose complex periodic or antiperiodic boundary conditions. The magnetostatic equations are solved using the vector or scalar potential formulations. In order to show the possibilities of the proposed approach, an example of application is studied and the results are discussed. 
[56] Single and Double Lagrange multipliers approaches applied to the Scalar potential formulation used in magnetostatic FEM Przeglad Elektrotechniczny, Vol. 5, 05/2010, Abstract AUBERTIN Mathieu, HENNERON Thomas, BOITEAU Olivier, PIRIOU Francis, GUERIN Pierre 
In this paper, we propose to introduce the single and double Lagrange multipliers approaches in the case of the finite element method (FEM). These approaches allow nonconforming meshes to be linked together. The methods introduced are developed in the case of a magnetostatic problem solved by the scalar potential formulation. An application is studied and the results obtained by both approaches are compared. 
[57] SourceField Method for 3D Magnetostatics: Influence of the Potential Created by the Exciting Currents JOURNAL OF MICROWAVES, OPTOELECTRONICS AND ELECTROMAGNETIC APPLICATIONS, Vol. 8, N°. 1, pages. 135142, 06/2009 HENNERON Thomas, PIRIOU Francis, TOUNZI Abdelmounaïm, CLENET Stéphane, BASTOS João Pedro Assumpção 
[58] Electromagnetic modelling of short circuited coreplates The international Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), Vol. 28, N°. 3, pages. 762771, 02/2009, URL, Abstract ROGER JeanYves, VRIGNAUD Emmanuel, HENNERON Thomas, BENABOU Abdelkader, DUCREUX JeanPierre 
Coreplates in large generators may suffer from local short circuits. An accurate analysis is required to avoid these failures and detect them when occurring. The purpose of this paper is to develop a lamination stack model compliant with interlamination default analysis. 
[59] Discrete finite element characterizations of source fields for volume
and boundary constraints in electromagnetic problems Journal of Computational and Applied Mathematics, Vol. 215, N°. 2, pages. 438447, 06/2008 HENNERON Thomas, CLENET Stéphane, DULAR Patrick, PIRIOU Francis 
[60] Analysis of a rotational single sheet tester using 3D Finite Element model taking into account hysteresis effect The international Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), Vol. 26, N°. 4, pages. 10371048, 08/2007, URL, Abstract LEITE Jean Vianei, BENABOU Abdelkader, DA SILVA Pedro Armando, SADOWSKI Nelson, HENNERON Thomas, CLENET Stéphane, KUOPENG Patrick, PIRIOU Francis, BATISTELA N.J. 
The accuracy of the magnetic field strength estimation in rotational single sheet tester is investigated with the finite element method and measurements. The incorporation of a vector hysteresis model, derived from the original scalar JilesAtherton model, in a finite element magnetic field code is performed. The application of this method leads to use the differential reluctivity tensor that arises naturally from the vector model. The effect of the shielding on a Rotational Single Sheet Tester is analyzed in order to improve the field homogeneity in the sample area. 
[61] Source Field Computation in NDT Applications IEEE Trans. Mag., Vol. 43, N°. 4, pages. 17851788, 04/2007 HENNERON Thomas, LE MENACH Yvonnick, PIRIOU Francis, CLENET Stéphane, DUCREUX JeanPierre 
[62] Computation of the magnetic flux in the finite elements method European Physical Journal Applied Physics, Vol. 39, pages. 119128, 03/2007, URL, Abstract HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
For designers, calculation of local fluxes can be very useful. In the vector potential formulation, the local fluxes can be easily deduced. In the scalar potential formulation, the determination of these fluxes presents some difficulties. In this paper, we present three methods to compute a flux through any surface in the scalar potential formulation. These are compared with the one used in the vector potential formulation for two application examples. 
[63] Calculation of Extra Copper Losses with Imposed Current Magnetodynamic Formulations IEEE Transaction on Magnetics, Vol. 42, N°. 2, 04/2006 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
[64] Dual Finite Element Formulations for Lumped Reluctances Coupling IEEE Transaction on Magnetics, Vol. 41, N°. 5, 01/2005 DULAR Patrick, GYSELINCK Johan, HENNERON Thomas, PIRIOU Francis 
[65] Comparison 3D magnetodynamic formulations in term of potential with imposed electric global quantities COMPEL, Vol. 23, N°. 4, 04/2004 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
[66] Evaluation of 3D finite element method to study and design a soft magnetic composite machine IEEE Transaction on Magnetics, Vol. 40, N°. 2, pages. 786789, 04/2004 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis, CROS Jérôme, VIAROUGE Philippe 
[67] 3D approaches to determine the end winding inductances of a PMLSM IEEE Trans. Mag, Vol. 38, N°. 2, pages. 989992, 03/2004 TOUNZI Abdelmounaïm, HENNERON Thomas, LE MENACH Yvonnick, ASKOUR Rachid, DUMETZ Eric 
[68] Estimation of numerical errors due to time and space discretisation IEEE Transactions on Magnetics, Vol. 40, N°. 2, pages. 1061  1064, 03/2004 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
ACT Conférence internationale avec acte 
[1] Finite Element Analysis of a Magnetomechanical Coupling Due to Punching Process in Electrical Steel Sheet CEFC 2020,Piza, Italy, 11/2020 M'ZALI Nabil, HENNERON Thomas, BENABOU Abdelkader, MARTIN Floran, BELAHCEN Anouar 
[2] Determination of stress dependent magnetostriction from a macroscopic magnetomechanical model and experimental magnetization curves SMM 2019, Poznan, Poland, 09/2019 M'ZALI Nabil, MARTIN Floran, AYDIN Ugur, BELAHCEN Anouar, BENABOU Abdelkader, HENNERON Thomas 
[3] Model Order Reduction Techniques applied to Magnetodynamic Scalar Potential Formulation ISEF2019 (Nancy, France), 08/2019 MULLER Fabian, CRAMPEN Lucas, HENNERON Thomas, CLENET Stéphane, HAMEYER Kay 
[4] Adaptive Stopping Criterion of PGD for Edge Elements based on Equilibrated Error Estimates in Magnetostatic Problems COMPUMAG 2019, Paris, France, 07/2019 YAN Shuai, TANG Zuqi, HENNERON Thomas, REN Zhuoxiang 
[5] StructurePreserved POD for Parametric Low Frequency Fullwave Problems with Gauged Potential Formulations COMPUMAG 2019, Paris, France, 07/2019 YAN Shuai, TANG Zuqi, HENNERON Thomas, REN Zhuoxiang 
[6] Separated Representation of the FE solution of the Nonlinear Magnetostatic Problem based on NonIntrusive PGD COMPUMAG 2019, Paris, France, 07/2019 HENNERON Thomas, CARON Guillaume, CLENET Stéphane 
[7] Surrogate Model based on the POD combined with the RBF Interpolation of Nonlinear Magnetostatic FE model COMPUMAG 2019, Paris, France, 07/2019 HENNERON Thomas, PIERQUIN Antoine, CLENET Stéphane 
[8] Error Estimators for Proper Generalized Decomposition (PGD) in Time Dependent Electromagnetic Field Problems COMPUMAG 2019, Paris, France, 07/2019 MULLER Fabian, HENNERON Thomas, CLENET Stéphane, HAMEYER Kay 
[9] Finite Element Modeling of Magnetic Properties Degradation Due to Plastic Deformation COMPUMAG 2019, Paris, France, 07/2019, Abstract M'ZALI Nabil, HENNERON Thomas, BENABOU Abdelkader, MARTIN Floran, BELAHCEN Anouar, SUNDARIA Ravi 
In this work a simulation of the effect of punching process on the magnetic properties of electromagnetic device is presented. The anhysteretic Sablik model is identified from measurements and implemented in a finite element code. A new model for magnetostriction is proposed. A mechanical punching process is simulated using the software ABAQUS, the plastic strain distribution near the punching edge is evaluated. The effect of punching process on the distribution of magnetic flux density and the magnetization current in an induction machine is analyzed. 
[10] 3D Numerical Modelling of Clawpole Alternators with its Electrical Environment COMPUMAG 2019, Paris, France, 07/2019 CARON Guillaume, HENNERON Thomas, PIRIOU Francis, FAVEROLLE Pierre, MIPO JeanClaude 
[11] Model Order Reduction based on Augmented Dynamic Mode Decomposition applied to magnetodynamic problems COMPUMAG 2019, Paris, France, 07/2019 CARON Guillaume, HENNERON Thomas 
[12] Accuracy of homogenization techniques to model lamination stacks with interlaminar currents COMPUMAG 2019, Paris, France, 07/2019 SABARIEGO Ruth, GYSELINCK Johan, LE MENACH Yvonnick, HENNERON Thomas 
[13] 3D coupled electromagneticfluidthermal analysis and experiment of 10kV oilimmersed triangular wound core transformer 2019 Joint MMMIntermag, January 1418, 2019 Washington, DC, 01/2019 GONG Ruohan, TANG Zuqi, WANG Shuhong, HENNERON Thomas, RUAN Jiangjun 
[14] Application Limits of the Airgap Maxwell Tensor CEFC 2018, 10/2018, Abstract PILE Raphaël, PARENT Guillaume, DEVILLERS Emile, HENNERON Thomas, LE MENACH Yvonnick, LE BESNERAIS Jean, LECOINTE JeanPhilippe 
In an electrical machine, the Maxwell Tensor is widely used to compute global forces or local pressure along a surface in
the air. This communication proposes to highlight the limits of the method with an academic case of slotless stator and rotor.
In particular an analytic demonstration shows the existence of coefficients depending on the geometry and the wavenumber
between the application of the Maxwell Tensor in the airgap and the stator magnetic pressure. 
[15] Application of UNet Network and Training Strategy to Optimal Mesh Refinement in Computational Electromagnetism CEFC 2018, Hangzhou, China, 10/2018 TANG Zuqi, SHEN Xi, HENNERON Thomas 
[16] Selection Methods of Components for the (D)EIM with Reduced Model of Nonlinear Magnetostatic Model Based on the POD CEFC 2018, Hangzhou, Chine, 10/2018 MONTIER Laurent, HENNERON Thomas, CLENET Stéphane 
[17] Employment of the FixedPoint Technique to Retain the Geometrical Periodicity Advantages in a nonLinear Modeling of Electrical Machines CEFC 2018, Hangzhou, Chine, 10/2018 AL EIT Moustafa, CLENET Stéphane, HENNERON Thomas 
[18] Mesh Deformation based on Radial Basis Function Interpolation applied to Low Frequency Electromagnetic Problem CEFC 2018, Hangzhou, Chine, 10/2018 HENNERON Thomas, PIERQUIN Antoine, CLENET Stéphane 
[19] GappyPOD versus DEIM reducedorder model of a nonlinear magnetodynamic problem SCEE2018, Taormina, Sicile, Italie, 09/2018 HASAN Rokibul, MONTIER Laurent, HENNERON Thomas, SABARIEGO Ruth 
[20] Reduced order model coupling with power system simulation software EMF 2018, Darmstadt, Germany, 04/2018 PIERQUIN Antoine, HENNERON Thomas, EL AKOUM Ali, FRATILA Mircea 
[21] Gappy POD based ROM of a NonLinear Eddy current problem EMF 2018, Darmstadt, Germany, 04/2018 HASAN Rokibul, MONTIER Laurent, HENNERON Thomas, SABARIEGO Ruth 
[22] Harmonicbalance finiteelement homogenisation of laminated iron cores with net circulating currents EMF 2018, Darmstadt, Germany, 04/2018 SABARIEGO Ruth, GYSELINCK Johan, LE MENACH Yvonnick, HENNERON Thomas 
[23] Finite Element (FE) ModelOrder Reduction of an Electrical Machine through Exploitation of Geometrical Symmetry Conférence EMF 2018, 02/2018 AL EIT Moustafa, CLENET Stéphane, HENNERON Thomas 
[24] Offline/Online approach based on POD and (D)EIM for the Model Order Reduction of Low frequency Electromagnetic devices ACOMEN 2017 (gent, belgique), 09/2017 HENNERON Thomas, MONTIER Laurent, PIERQUIN Antoine, CLENET Stéphane 
[25] A method to model the short circuits in the lamination stack Acomen, Gand, 09/2017 ZIANI Smail, HENNERON Thomas, LE MENACH Yvonnick 
[26] Model order reduction of an electrical machine controlled with an error indicator Oral Session, COMPLAS 2017, Barcelonne, Espagne, 09/2017 MONTIER Laurent, HENNERON Thomas, CLENET Stéphane, GOURSAUD Benjamin 
[27] Exploitation of Geometrical Symmetry towards a reduction of the Linear Finite Element Modeling of Rotating Machines Conférence NUMELEC 2017, 07/2017 AL EIT Moustafa, CLENET Stéphane, HENNERON Thomas 
[28] Application of the Proper Generalized Decomposition to Solve MagnetoElectric Problem COMPUMAG2017 (Daejeon, Corée du sud), 06/2017 HENNERON Thomas, CLENET Stéphane 
[29] Datadriven model order reduction for magnetostatic problem coupled with circuit equations COMPUMAG 2017, Daejeon, Korea, 06/2017 PIERQUIN Antoine, HENNERON Thomas, CLENET Stéphane 
[30] Proper Generalized Decomposition Applied on a Rotating Electrical Machine Oral Session, COMPUMAG 2017, Daejon, South Korea, 06/2017 MONTIER Laurent, HENNERON Thomas, CLENET Stéphane, GOURSAUD Benjamin 
[31] Nonlinear Lamination Stacks Studied with Harmonic Balance FEM combined with Homogenization approach Compumag (International Conference on the Computation of Electromagnetic Fields), 03/2017, Abstract ZIANI Smail, HENNERON Thomas, LE MENACH Yvonnick 
Harmonic Balance Finite Element method combined with homogenization method is used to model lamination stacks. The Harmonic Balance gives directly the steadystate solution and the homogenization method reduces the number of unknowns. The numerical model takes into account the nonlinear magnetic behavior and the electric conductivity. The results of the proposed method are compared with those obtained from a classic approach. 
[32] Numerical Modeling of Steady State of Magnetostatic Problems Coupled with nonlinear Electric Circuit Conférence CEFC 2016, Miami, 11/2016, 11/2016 CARON Guillaume, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
[33] Nonlinear Lamination Stacks Studied with Harmonic Balance FEM Supplied by Magnetic Flux Arising from PWM CEFC 2016, Miami, 11/2016, Abstract ZIANI Smail, HENNERON Thomas, LE MENACH Yvonnick 
The Harmonic Balance combined with the finite element method enables to obtain the steadystate solution of electromagnetic problems. In this communication, we propose to apply this approach to study a laminated iron core submitted to a magnetic flux arising from a Pulse Width Modulation (PWM) voltage. The proposed numerical model takes into account the nonlinear magnetic behaviour, the electric conductivity and a short circuit between steel sheets. 
[34] Rotation movement based on the Spatial Fourier Interpolation Method (SFIM) CEFC 2016, Miami, USA, 11/2016, Abstract MONTIER Laurent, CLENET Stéphane, HENNERON Thomas, GOURSAUD Benjamin 
In the field of computational electromagnetics, taking into account the rotation of a subdomain is required to simulate certain devices such as electrical machines. We propose a sliding surface method based on a spatial Fourier interpolation in order to take into account any rotation angle with a very simple numerical implementation. 
[35] Optimization of the TEAM workshop problem 22 using PODEIM reduced model CEFC 2016, Miami, Florida, USA, 11/2016 PIERQUIN Antoine, BRISSET Stéphane, HENNERON Thomas, CLENET Stéphane 
[36] Comparison of DEIM and BPIM to Speed up a PODbased Nonlinear Magnetostatic Model CEFC 2016 (Miami, USA), 11/2016 HENNERON Thomas, MONTIER Laurent, PIERQUIN Antoine, CLENET Stéphane 
[37] Parametric analysis of Magnetoharmonic problem based on Proper Generalized Decomposition CEFC 2016 (Miami, USA), 11/2016 HENNERON Thomas, CLENET Stéphane 
[38] Structure Preserving Model Reduction of Low Frequency Electromagnetic Problem based on POD and DEIM CEFC 2016, Miami, Florida, USA, 11/2016, Abstract MONTIER Laurent, PIERQUIN Antoine, HENNERON Thomas, CLENET Stéphane 
The Proper Orthogonal Decomposition combinedwith the (Discrete) Empirical Interpolation Method can be used to reduce the size of a numerical model. To conserve robustness, the reduced model must be constructed by preserving the structure of the full model. In this communication, an approach is proposed with potential formulations used to solve electromagnetic problems. 
[39] OFFLINE MODEL ORDER REDUCTION FOR ONLINE APPROACH OF LOW FREQUENCY ELECTROMAGNETIC DEVICES BASED ON POD AND (D)EI METHODS Conférence EMIIC (Engineering Mechanics Institute Conference, Metz, France), 10/2016 HENNERON Thomas, MONTIER Laurent, PIERQUIN Antoine, CLENET Stéphane 
[40] A coupled method between homogenization and vector potential formulations
to model shortcircuits in lamination stacks MSHOM 2016, Vienna, 09/2016 ZIANI Smail, HENNERON Thomas, LE MENACH Yvonnick 
[41] Waveform RelaxationNewton Method to determine Steady State Operation: Application to threephase transformer Conference EPNC 2016, Helsinki, 06/2016, Abstract CARON Guillaume, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
This paper presents a 3D finite element method to determine the steady state operation for magnetostatic problems coupled with electrical circuit equations. For this purpose, the waveform relaxation method combined with the Newton method (WRNM) is developed. This method is especially suitable to long transient problems. To show the efficiency of this approach a threephase transformer is studied. The results show that the WRNM becomes very efficiency when the transient state is more important than about 10 periods. 
[42] Harmonic Balance Finite Element Method applied for Nonlinear Lamination stack with short circuits EPNC 2016, Helsinki, 06/2016, Abstract ZIANI Smail, MONTIER Laurent, HENNERON Thomas, LE MENACH Yvonnick 
In this paper, the Harmonic Balance Method is used to obtain the steadystate solution of a laminated iron core with an imposed magnetic flux. The numerical model takes into account the nonlinear magnetic behaviour, the electric conductivity and a short circuit between steel sheets. The results of the Harmonic Balance Method are compared with those obtained from a classic approach. 
[43] Proper Generalized Decomposition Method Applied to Solve 3D Low Frequency Electromagnetic Field Problems FEM2016 (Florence, Italie), 05/2016 HENNERON Thomas, CLENET Stéphane 
[44] Geometrical parametric model order reduction of transmission lines EMF 2016, Lyon, France, 04/2016 PIERQUIN Antoine, HENNERON Thomas, LE MENACH Yvonnick, COLAS Frédéric 
[45] Waveform Relaxation Method combined with Proper Orthogonal Decomposition to solve linear magnetodynamic steady state problem coupled with electric circuit Conférence EMF 2016, Lyon, 04/2016 CARON Guillaume, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
[46] A method coupling a modified vector potential A* and a homogenization formulations to
model short circuits in lamination stacks EMF 2016, Lyon, 04/2016 ZIANI Smail, LE MENACH Yvonnick, HENNERON Thomas 
[47] Robust model order reduction of a nonlinear electrical machine at startup through reduction error estimation EMF 2016, 04/2016 MONTIER Laurent, HENNERON Thomas, GOURSAUD Benjamin, CLENET Stéphane 
[48] Eddy current computation in 2DFEM for permanent magnet loss calculation Compumag 2015, Montreal, Canada, 07/2015 BOUGHANMI Walid, HENNERON Thomas, BENABOU Abdelkader, TOUNZI Abdelmounaïm, ZAÏM Mohamed El Hadi 
[49] Comparison of Model Order Reduction Methods like POD, CVT,
ArnoldiKrylov and PGD to solve quasistatic problems COMPUMAG 2015, 07/2015, Abstract MONTIER Laurent, HENNERON Thomas, GOURSAUD Benjamin, CLENET Stéphane 
In the domain of numerical computation, Model Order Reduction (MOR) methods are more and more applied in mechanics and
have shown their efficiency in terms of computation time and memory requirements. In computational electromagnetics, research
has started recently and the different methods available in the literature need to be compared in order to find the most efficient
one. We propose to evaluate MOR approaches in order to solve linear magnetoquasistatic field problems. Therefore, the Proper
Orthogonal Decomposition (POD), the Centroidal Voronoi Tessellation (CVT), the Proper Generalized Decomposition (PGD) and the
ArnoldiKrylov projection (AKP) are developed and compared. 
[50] Balanced Proper Orthogonal Decomposition applied to
magnetoquasistatic problems COMPUMAG 2015, 07/2015, Abstract MONTIER Laurent, HENNERON Thomas, GOURSAUD Benjamin, CLENET Stéphane 
Model Order Reduction (MOR) methods are an active research field in the numerical analysis domain. They are applied to many
different areas in physics, especially in mechanics because they allow to dramatically reduce the computational time. MOR is quite
recent in electromagnetics and needs still to be investigated. The Proper Orthogonal Decomposition (POD) is the most famous one
and has already shown very promising results. However, the POD approach minimizes the error in the L2 sense on the whole domain
and cannot be very accurate to calculate quantities of interest, like flux associated with a probe in region where the field is low. In
this communication, we present the Balanced Proper Orthogonal Decomposition (BPOD) which extends the POD by taking account
of probes in its model. The BPOD and POD approaches will be compared on a 3D linear magnetoquasistatic field problem. 
[51] Multirate coupling of controlled rectifier and nonlinear finite element model based on Waveform Relaxation Method COMPUMAG 2015, Montréal, Québec, Canada, 06/2015 PIERQUIN Antoine, HENNERON Thomas, BRISSET Stéphane, CLENET Stéphane 
[52] Multidisciplinary optimization formulation to the optimization of multirate systems COMPUMAG 2015, Montréal, Québec, Canada, 06/2015 PIERQUIN Antoine, BRISSET Stéphane, HENNERON Thomas 
[53] Application of the PGD and DEI methods to solve a NonLinear Magnetostatic Problem coupled with the Circuit Equations COMPUMAG 2015, Montréal, Québec, Canada, 06/2015 HENNERON Thomas, CLENET Stéphane 
[54] SpaceTime Galerkin Projection of ElectroMagnetic Fields COMPUMAG 2015, Montréal, Québec, Canada, 06/2015 WANG Zifu, HENNERON Thomas, HOFMANN Heath 
[55] Time periodicity condition of magnetostatic problem coupling with electric circuit imposed by Waveform Relaxation Method Conférence Compumag 2015, Montreal, 06/2015, URL, Abstract CARON Guillaume, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
In numerical computation, the finite element (FE) method associated with external electric circuits is often used to evaluate electromagnetism devices with voltage sources. To study the solution of the steady state, the computation time can be prohibitive due to a large transient state compared with the time step used to discretize the time domain. In this communication, the Waveform Relaxation Method is developed to impose the steady state of the solution in the case of magnetostatic problem coupled with electric cricuit equation. 
[56] Reduction of a Finite Element Parametric Model using Adaptive POD Methods COMPUMAG 2015, Montréal, Québec, Canada, 06/2015 CLENET Stéphane, HENNERON Thomas, IDA Nathan 
[57] Model order reduction of single transformer based on typical engineer testoriented POD (TETOPOD) methods EPNC2014 (Pilsen), 07/2014 HENNERON Thomas, CLENET Stéphane 
[58] Model Order Reduction of Multiinput NonLinear systems based on PODDEI Methods CEFC2014, 05/2014 HENNERON Thomas, CLENET Stéphane 
[59] Energetic MeshtoMesh Projection of Magnetic Fields With Respect to Nonlinear BH Curves
CEFC 2014, Annecy, France, 05/2014 WANG Zifu, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
[60] Model order reduction of magnetoquasistatic problems based on POD and Arnoldibased Krylov methods CEFC 214, Annecy, France, 05/2014, Abstract PIERQUIN Antoine, HENNERON Thomas, CLENET Stéphane, BRISSET Stéphane 
Two model order reduction approaches are applied
to reduce the computational time of a quasistatic finite element
problem. Both methods are compared on an academic example. 
[61] Error estimation of POD reduced model  Application to a permanent magnet synchronous machine
CEM2014 (londres), 03/2014 HENNERON Thomas, CLENET Stéphane 
[62] Optimization process to solve multirate system ISEF 2013, Ohrid, Macedonia, 09/2013, Abstract PIERQUIN Antoine, BRISSET Stéphane, HENNERON Thomas, CLENET Stéphane 
The modeling of a multirate system formed by components with heteroge
neous time constants can be done using fixedpoint method. This method allows a time
discretization of each subsystem with respect to its own time constant. In an optimization
process, executing the loop of the fixedpoint at each model evaluation can be time consum
ing. By adding one of the searched waveform of the system to the optimization variables,
the loop can be avoided. This strategy is applied to the optimization of a transformer. 
[63] Model Order Reduction of NonLinear Magnetostatic Problems on POD and DEI Methods compumag2013, 07/2013 HENNERON Thomas, CLENET Stéphane 
[64] Energetic Galerkin projection of electromagnetic fields between different meshes
COMPUMAG 2013 Budapest, Hungary, 07/2013, Abstract WANG Zifu, TANG Zuqi, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
The Galerkin projection provides an useful tool to transfer electromagnetic fields between different meshes.
Given an electromagnetic field calculated on the source mesh, the transfer to a different mesh can be employed for modelcoupling, domain decomposition, remeshing, visualization and similar proposes.
The Galerkin projection consists of calculating a target field which minimizes the interpolation error between two discretized fields.
However, the $L^2$ Galerkin projection suffers from nonconservation of the electromagnetic energy.
In this paper, we present an energetic approach for Galerkin projections. 
[65] Benefits of waveform relaxation method and space mapping for the optimization of multirate system COMPUMAG 2013, Budapest, Hungary, 07/2013, Abstract PIERQUIN Antoine, BRISSET Stéphane, HENNERON Thomas, CLENET Stéphane 
For the optimization of a component from a multirate system, the article presents benefits of the joint use of several models for the optimization and of fixedpoint strategy for the modeling. Thus, space mapping allows reducing time computation of an optimization process by limiting the number of evaluations of time consuming models. In the case of multirate problems, these models can be modeled by Waveform Relaxation Method to provide an additional time saving. 
[66] Comparison of implementation techniques for Galerkin projection between different meshes EMF, 05/2013, Abstract WANG Zifu, HENNERON Thomas, DULAR Patrick, MIPO JeanClaude, PIRIOU Francis 
Usually, coupled problems (e.g. magnetomechanical or magnetothermal problems) with weak interactions can be decomposed into several subproblems and solved separately. However, in the area of finite element computation, depending on the nature of the subproblem to solve, the used meshes generally differ. In this case, transfers of fields are required to take into account the interaction between the subproblems. Given a previouslycomputed field, in order to obtain on the target mesh its approximate image, the Galerkin projection enjoys several advantages over interpolation, especially in terms of precision. This method consists of minimizing the norm of the interpolation error in the chosen target space. The accuracy of the solution is ensured by the quasibest property of the Galerkin method.
Nevertheless, in practice the general implementation of the Galerkin projection has been proved challenging. As the source and target fields are discretized on different meshes, the accurate assembly of the projection system necessitates the numeric integrating over an intermediate mesh. In practice, such an intermediate mesh can be calculated by means of intersecting the source and target meshes. However, the use of intersection requires heavy work on programming and high computation cost (P.E. Farrell and J.R. Maddison, â€Conservative interpolation between volume meshes by local Galerkin projectionâ€, in Comput. Methods Appl. Mech Engrg, Vol. 200, pp 89100, 2009).
This proposed paper discusses the possibility to avoid mesh intersections, by using an approximate integrating algorithm. Instead of integrating over the lowest common mesh, the integrals are computed over the target mesh. Over the quadrature points of targets elements, the source solution is interpolated and approximately integrated. This is less accurate than integrating over intersections. However, the accuracy can be improved using highoder quadrature rules. Through analytical field distributions such as skin effect current densities, we have compared this approximate method to the intersection method, on node, edge and facet Whitney elements. The robustness of the approximate method will also be studied using reciprocal projection between fine and coarse meshes. In our examples of projection on edge elements, the computation time can be reduced by a factor up to one hundred. Meanwhile, the lost accuracy is less than 0.6%. The integration of physical constraints in the projection formulation will be shown to improve coarsetofinemesh projected solutions.

[67] Waveform relaxation method and proper orthogonal decomposition approach to solve multirate electromagnetic system EMF 2013, Bruges, Belgium, 04/2013, Abstract PIERQUIN Antoine, HENNERON Thomas, CLENET Stéphane, BRISSET Stéphane 
In the communication, the WRM and the POD techniques are applied to study a
transformer supplied by a power converter. The transformer is modeled by Finite
Element Method. A reduced model of the transformer provided by the POD tech
nique is used to couple the power converter and the transformer using the WRM
technique. 
[68] Model order reduction applied to the numerical study of electrical motor
based on POD method EMF2013, 04/2013 HENNERON Thomas, CLENET Stéphane 
[69] Influence of excitation on Energy bounds of dual potential formulations in magnetostatics CEFC 2012 Oita, Japan, 11/2012 CLENET Stéphane, HENNERON Thomas 
[70] Model Order Reduction of Electromagnetic Field Problem Coupled with Electric Circuit Based on Proper Orthogonal Decomposition OIPE, 09/2012 HENNERON Thomas, CLENET Stéphane 
[71] Proper Generalized Decomposition method applied to the magnetic simulation of a SMC microstructure INTERMAG2012, 05/2012 HENNERON Thomas, BENABOU Abdelkader, CLENET Stéphane 
[72] Stochastic model in eddy current non destructive testing EPE2011 (Birmingham), 09/2011 HOMBERG Charles, HENNERON Thomas, CLENET Stéphane 
[73] Interlaminar shortcircuit detection: modeling of the El Cid test and
comparison with the experiment ISEF 2011 Madeira, Portugal, 09/2011, Abstract MÜLLER JulianaLuisa, ROMARY Raphaël, BENABOU Abdelkader, HENNERON Thomas, PIRIOU Francis, BASTOS João Pedro Assumpção, ROGER JeanYves 
Shortcircuits in turbogenerator stators can lead to a modification of the magnetic flux
distribution that impact the performances and, in some extreme cases, to local damage of the iron core.
This work presents the modeling of shortcircuited laminations in a stator yoke of a turbogenerator. A 3D
finite element (FE) model, associated to a homogenization technique, is used to calculate the shortcircuit
current. The results are compared with the experiment, especially for the electrical signature of the
diagnosis test known as Electromagnetic Core imperfection detector (El Cid). 
[74] A TIMEDOMAIN IMPLICITSCHEMA DIRECT SOLVER: APPLICATION TO FINITE INTEGRATION SOLUTION
ISEF 2011, 09/2011, Abstract WANG Zifu, LE MENACH Yvonnick, TANG Zuqi, KORECKI Julien, HENNERON Thomas 
In timedomain electromagnetic fields computation, numerical methods (such as Finite Element
Method (FEM), Finite Integration Technique (FIT) [13] and etc.) have been applied. For the time
domain integration solution, explicit and implicit schemas have been widely used.
In comparison with implicit methods, the explicit methods are easier to realize in terms of
computation complexity, however, they are constrained by the stability condition. This condition
may require a small time step and therefore a prohibitive computing time. Another possibility is to
use an implicit schema which ensures the numerical stability. Unfortunately the implicit methods
require equation solved at each time step [4]. As a consequence, despite of a free choice on time
step, the computation time using the full implicit methods increases.
In this paper, fixedpoint explicit calculation is introduced to an implicit schema. This method
combines the two advantages of implicit and explicit methods: no stability condition and no
equation solving. The solver is then applied to a timedomain eddy current problem. Using
orthogonal mesh cells and FIT, the massmatrices in discrete formulations are diagonal. The fixed
point explicit method allows direct calculations without matrix inversion or decomposition.

[75] Proper Generalized Decomposition method to solve Quasi Static Field Problems COMPUMAG2011, 07/2011 HENNERON Thomas, CLENET Stéphane 
[76] 3D FE Modelling of Interlamination Shortcircuits Taking into Account the
Building Bar COMPUMAG 2011 Sydney, Australie, 07/2011, Abstract MÜLLER JulianaLuisa, BENABOU Abdelkader, HENNERON Thomas, PIRIOU Francis, BASTOS João Pedro Assumpção, ROGER JeanYves 
This paper deals with the modelling of a
lamination stack, crossed by a conducting building bar, in the
presence of an interlamination shortcircuit. Under a timevarying
magnetic flux, an induced current loop flows through
both the building bar and the fault. To reduce computational
times, a homogenization technique is used to model the
lamination stack. Eddy current losses and total magnetic
energy values are compared for cases with and without
homogenization for 50 Hz and 100 Hz. 
[77] Evaluation of the overlapping finite element method for taking into account very small displacements IGTE, 09/2010 KREBS Guillaume, TOUNZI Abdelmounaïm, HENNERON Thomas 
[78] Influence of the approximation function of the vector potential formulation with the Lagrange multipliers approach and the Mortar method EPNC 2010, Essen, Allemange, 07/2010, Abstract AUBERTIN Mathieu, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
In this paper, we propose to compare two types of approximation of the vector potential used to solve a magnetostatic problem in the case of the domain decompostion. The single and Lagrange multipliers approaches and the Mortar method are considered in this context. 
[79] NonLinear Analytical Model of a Three Phase Transformer
Based on 2DFEM Identification of its Reluctances EPNC 2010, Essen, Allemagne, 06/2010, Abstract FRATILA Mircea, BENABOU Abdelkader, HENNERON Thomas 
This paper presents a simple model to simulate the
currents in a transformer, especially during the transient state.
The model is based on a reluctance circuit using a finite element
(FE) tool for identifying the global behaviour laws of the
transformer iron core. A threephase threelimb transformer is
modelled to test the proposed approach. 
[80] Preconditioner for Mortar method applied to the FEM CEFC 2010, 05/2010 TINZEFTE Abdellatif, AUBERTIN Mathieu, HENNERON Thomas, PIRIOU Francis 
[81] Overlapping finite elements used to connect nonconforming meshes in 3D with a vector potential formulation CEFC 2010, 05/2010 KREBS Guillaume, HENNERON Thomas, CLENET Stéphane, LE BIHAN Yann 
[82] An approach to determine the circulation of magnetic field in FEM computation code with vector potential formulation CEFC 2010, 05/2010 HENNERON Thomas, PIRIOU Francis 
[83] Study of Different FEM Models to Analyze Homogenized Iron Lamination with Electrical Fault Compumag 2009, Florianopolis, Brésil, 11/2009, Abstract MÜLLER JulianaLuisa, BENABOU Abdelkader, HENNERON Thomas, PIRIOU Francis, BASTOS João Pedro Assumpção, ROGER JeanYves 
In this paper we compare different approaches for the lamination stack homogenization with a shortcircuit due to an electrical fault between several sheets. The presented techniques are based on the determination of a complex equivalent magnetic permeability for the homogenized domain. The eddy current losses are calculated in the homogenized lamination stack and in the fault. These losses are compared with those obtained from a reference system where the lamination is modeled with its real geometry. 
[84] Periodic and Antiperiodic boundary conditions with the Lagrange multipliers in the FEM Compumag 2009, Florianopolis, Brésil, 11/2009 AUBERTIN Mathieu, HENNERON Thomas, PIRIOU Francis, GUERIN Pierre, MIPO JeanClaude 
[85] Comparison between Overlapping method and Lagrange multipliers approach applied to a movement EMF’09 (Mondovi, Italy), 05/2009 HENNERON Thomas, KREBS Guillaume, AUBERTIN Mathieu, CLENET Stéphane, PIRIOU Francis 
[86] Décomposition de domaines dans les problèmes de magnétostatique résolus par la
méthode des éléments finis Numélec 2008 Liège, 11/2008 AUBERTIN Mathieu, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude, GUERIN Pierre 
[87] Identification of a 7phase clawpole starteralternator
for a microhybrid automotive application
International Conference on Electrical Machines (ICEM08), 09/2008, Abstract BRUYERE Antoine, HENNERON Thomas, LOCMENT Fabrice, SEMAIL Eric, BOUSCAYROL Alain 
This paper deals with the identification of a new high power starteralternator system, using both: a Finite Element Method (FEM) modeling and an elementary experimental vector control. The drive is composed of a synchronous 7phase clawpole machine supplied with a low voltage / high current Voltage Source Inverter (VSI). This structure needs specific approaches to plan its electrical and mechanical behaviors and to identify the parameters needed for control purpose. At first, a Finite Element Method (FEM) modeling of the machine is presented. It is used for the predetermination of the electromotive forces and of the torque. Experimental results are in good accordance with numerical results. In a second part, resistive and inductive parameters of the drive are determined by an original experimental approach that takes into account each component of the drive: the battery, the VSI and the machine. 
[88] 3D Study of an Electrostatic MEMS
device taking account of the active part displacement CEFC 2008, 05/2008, Abstract BOLONI Francisc, KREBS Guillaume, HENNERON Thomas, TOUNZI Abdelmounaïm 
The analysis of microelectromechanical systems (MEMS) requires to take into account both electric and mechanical phenomena. An iterative FEM approach, which involves the computation of the electrostatic field and the displacement of the moving part, is presented. The maximum displacement allows computing the pullin voltage. 
[89] Predetermination of Currents and Field in ShortCircuit Voltage Operation for an AxialFlux Permanent Magnet Machine CEFC 2008 (Athene), 05/2008 HENNERON Thomas, LOCMENT Fabrice, SEMAIL Eric, PIRIOU Francis 
[90] Insulating layers in electrokinetics problem solved by the FEM ACOMEN 2008 (Liege), 05/2008 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
[91] Calculation of induction machine external field using both magnetodynamic potential formulations COMPUMAG 2007, 06/2007 ALLAERT YvesLaurent, HENNERON Thomas, CLENET Stéphane, ABAKAR Ali, MARCHAND Claude 
[92] Calcul de flux magnétique locaux avec la méthode des éléments finis NUMELEC’06, 11/2006 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
[93] Using 3DFEM for design of an axial flux sevenphase machine EMF 2006, 06/2006, Abstract LOCMENT Fabrice, HENNERON Thomas, SEMAIL Eric, PIRIOU Francis 
For the experimental sevenphase machine studied in this paper, parameters necessary for the control such as inductances and electromotive force (EMF) are sensitive to harmonics. A conventional analytical method in which only the first harmonic is taken into account does not give good results. Besides, the machine is an axialflux one and has two asymmetrical rotors: a 3DFEM is then necessary. Comparisons between predeterminations and experimental results show sufficient accuracy to achieve a control model. 
[94] Analysis of a rotational single sheet tester using 3d finite element model taking into account hysteresis effect EPNC 2006, Maribor, Slovenia, 06/2006 LEITE Jean Vianei, BENABOU Abdelkader, DA SILVA Pedro Armando, SADOWSKI Nelson, HENNERON Thomas, CLENET Stéphane, KUOPENG Patrick, PIRIOU Francis, BATISTELA N.J. 
[95] Influence of Source Fields on FEM Potential Formulations in Magnetostatics CEFC 2006, 03/2006 HENNERON Thomas, CLENET Stéphane, BASTOS João Pedro Assumpção, PIRIOU Francis 
[96] Calculation of global quantities using incidence matrix in the Aφ formulation CEM 2006, 02/2006 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
[97] Study of a PM planar actuator using a permeance network model and the 3DFEM COMPUMAG05, 09/2005, Abstract KREBS Guillaume, HENNERON Thomas, TOUNZI Abdelmounaïm, PAUWELS Brecht, WILLEMOT Dirk 
Specific actuators are now widely used. The design and study of such a converter must be carried out using specific
models. This paper deals with the study of a permanent magnet planar actuator with Multiple Degrees of Freedom (MdoF).
A 3D permeance network model is used to design the actuator and study its performance. The 3DFEM is also used to
investigate more accurately the prototype behavior. A prototype of the actuator has been built. Results, given by
both models are shown and compared with those obtained experimentally. 
[98] Comparison of different methods to estimate numerical errors in finite element problem coupled with external circuit equations CEM 2004, 01/2004 HENNERON Thomas, BOUILLAULT Frédéric, CLENET Stéphane, PIRIOU Francis 
[99] Analysis of supplementary conditions for a smooth torque running of heteropolar excited Vernier Reluctance Machines ISEF 2003, 01/2003 TAÏBI Soufiane, HENNERON Thomas, TOUNZI Abdelmounaïm 
ACN Conférence nationale avec acte 
[1] Modélisation d’empilements de tôles par une méthode de couplage entre une formulation A* spectrale et une approche homogénéisée JCGE 2017 (Jeunes Chercheurs en Génie Electrique), 06/2017, Abstract ZIANI Smail, HENNERON Thomas, LE MENACH Yvonnick 
Nous proposons une approche de couplage entre une formulation éléments finis spectrale et une approche d’homogénéisation afin de modéliser un empilement de tôles. L’approche spectrale permet d’obtenir directement le régime permanent, l’homogénéisation permet de réduire le nombre d’inconnues et la formulation classique nous permet de prendre en compte les effets de bord des tôles. Notre approche prend en compte une loi de comportement magnétique non linéaire et une conductivité électrique dans les tôles. Les résultats de notre approche de couplage sont comparés aux résultats d’une approche classique de type éléments finis pas à pas dans le temps. 
[2] Résolution d’un problème piézoélectrique par la méthode
« Proper Generalized Decomposition »
NUMELEC2015, St Nazaire, 06/2015 HENNERON Thomas, CLENET Stéphane 
[3] Réduction de modèle par POD appliquée à un transformateur planar en régime magnétoharmonique NUMELEC15  St Nazaire, 06/2015, Abstract TAYLOR Laurent, HENNERON Thomas, MARGUERON Xavier, LE MENACH Yvonnick, LE MOIGNE Philippe 
La prédétermination, dans la phase de dimensionnement, des pertes et des valeurs d’inductances est nécessaire à l’élaboration de composants magnétiques performants pour l’électronique de puissance. La modélisation numérique peut être utilisée pour déterminer les caractéristiques propres d’un composant notamment lorsque sa géométrie est "complexe" ou que la fréquence d’utilisation est élevée. Ces modèles sont très précis mais le temps de simulation nécessaire est important par rapport à des modèles analytiques plus simplistes. Les méthodes de réduction de modèles, type POD ou autres, permettent de diminuer le nombre de ces simulations numériques tout en conservant une grande précision. 
[4] Approche énergétique pour la projection de champs entre deux maillages non coïncidents Numélec 2012, 07/2012, Abstract WANG Zifu, HENNERON Thomas, PIRIOU Francis, MIPO JeanClaude 
Une méthode de projection de champs entre deux maillages non coïncidents basée sur une approche énergétique est développée. Cette approche est proposée en magnétostatique pour les deux formulations en potentiel classiquement utilisées. Un exemple académique permet de montrer les possibilités. 
[5] Application des méthodes POD et PGD à la résolution de problèmes magnétodynamiques NUMELEC2012, 07/2012 HENNERON Thomas, CLENET Stéphane 
[6] Une procédure pour simuler deux rotations indépendantes par la méthode Eléments Finis en 3D EF 2009 Compiègne, 09/2009 AUBERTIN Mathieu, HENNERON Thomas, TOUNZI Abdelmounaïm 
[7] Modélisation par éléments finis de capteurs de flux pour la caractérisation de l’hystérésis en champ tournant Proc. of MGE 2005, Lyon, France, 12/2005 BENABOU Abdelkader, HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
[8] Introduction des grandeurs globales électriques dans les formulations magnétodynamiques en potentiel JCGE 2005, 06/2005 HENNERON Thomas 
AP Autre publication 
[1] Review on Numerical Modeling of Magnetoelectric devices Newletters, International Compumag Society, Vol. 23, N°. 3, 11/2016 MININGER Xavier, HAKEIM Talleb, HENNERON Thomas 
INV Conférence invité 
[1] MODEL ORDER REDUCTION OF FINITE ELEMENT MODEL IN LOW FREQUENCY ELECTROMAGNETISM MORTech2017 (Seville, espagne), 11/2017 HENNERON Thomas 
[2] Modelling of magnetoelastic problems on disconnected meshes
Numélec 2012 Marseille, 07/2012, Abstract WANG Zifu, JOURNEAUX Antoine, HENNERON Thomas, BOUILLAULT Frédéric, NEMITZ Nicolas 
To compute the magnetoelastic problems, a chaining of
III. CALCUL DES FORCES
finite element calculations is realized. The coupling term is magnetic
Diverses mï¿½thodes peuvent ï¿½tre envisagï¿½es pour le calcul
force. To compute it and realize the chaining, various methods are ana
des forces : mï¿½thode des travaux virtuels, forces de Lorentz
lyzed. The approaches are then compared to an academic example with
[1, 2]. Ces diffï¿½rentes mï¿½thodes sont thï¿½oriquement ï¿½quiva
analytical solution.

[3] Accounting of different movements in the study of electomechanical devices using 3D FEM MOMAG 2008, 09/2008 TOUNZI Abdelmounaïm, LE MENACH Yvonnick, HENNERON Thomas, KREBS Guillaume, CLENET Stéphane 
[4] Numerical solutions of electrokinetic and magnetostatic problems with imposed
global quantities using FEM and FIT MOMAG06 (BeloHorizonte  BRESIL), 07/2006 HENNERON Thomas, KORECKI Julien, LE MENACH Yvonnick, CLENET Stéphane, PIRIOU Francis 
TH Thèse 
[1] Contribution à la prise en compte des grandeurs globales dans les problèmes d’électromagnétisme résolus avec la méthode des éléments finis 12/2004 HENNERON Thomas 
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