Fiche individuelle
Francis PIRIOU  
Titre  Professeur  
Equipe  Outils et Méthodes Numériques  
Téléphone  +33 (0)320434157  
Fax  +33 (0)320436967  
francis.piriou@univlille1.fr  
Publications 
ACLI Revue internationale avec comité de lecture 

[1] Two guaranteed equilibrated error estimators for Harmonic formulations in eddy current problems Computers & Mathematics with Applications, 10/2018, URL, Abstract CREUSE Emmanuel, LE MENACH Yvonnick, NICAISE Serge, PIRIOU Francis, TITTARELLI Roberta 
In this paper a guaranteed equilibrated error estimator is developed for the 3D harmonic magnetodynamic problem of Maxwell’s system. This system is recasted in the classical Aphi potential formulation and solved by the Finite Element method. The error estimator is built starting from the Aphi numerical solution by a local flux reconstruction technique. Its equivalence with the error in the energy norm is established. A comparison of this estimator with an equilibrated error estimator already developed through a complementary problem points out the advantages and drawbacks of these two estimators. In particular, an analytical benchmark test illustrates the obtained theoretical results and a physical benchmark test shows the efficiency of these two estimators. 
[2] Canal Lock Variable Speed Hydropower Turbine Design and Control IET Renewable Energy Generation, 08/2018, URL ZHANG Jian, LEONTIDIS Vlasios, DAZIN Antoine, TOUNZI Abdelmounaïm, DELARUE Philippe, CAIGNAERT Guy, PIRIOU Francis, LIBAUX Antoine 
[3] Comparison of Numerical Error Estimators for Eddy Current Problems solved by FEM IEEE Transactions on Magnetics, Vol. 54, N°. 3, pages. 7401204, 03/2018, Abstract TITTARELLI Roberta, LE MENACH Yvonnick, PIRIOU Francis, CREUSE Emmanuel, NICAISE Serge, DUCREUX JeanPierre 
In the domain of field computation with the finite element method, choosing the mesh refinement is an important step to obtain an accurate solution. In order to evaluate the quality of the mesh, a posteriori error estimators are frequently used. In this communication we propose to analyze and to compare residual and equilibrated error estimators for eddy current problems in the case of Aφ and TΩ formulations. The different properties of the estimators will be discussed. 
[4] Quantitative Design of a High Performance Permanent Magnet
Vernier Generator IEEE Transactions on Magnetics, Vol. 53, N°. 11, 11/2017 ZHANG Jian, TOUNZI Abdelmounaïm, DELARUE Philippe, PIRIOU Francis, LEONTIDIS Vlasios, DAZIN Antoine, CAIGNAERT Guy, LIBAUX Antoine 
[5] 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 
[6] 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. 
[7] A posteriori residual error estimators with mixed boundary conditions for quasistatic electromagnetic problem The International Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), Vol. 34, N°. 3, pages. 724739, 07/2015, URL TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis, NEMITZ Nicolas 
[8] Residual a posteriori estimator for magnetoharmonic potential formulations with global quantities for the source terms IEEE Transactions on Magnetics, Vol. 51, N°. 3, 06/2015, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis 
In the modeling of eddy current problems, potential formulations are widely used in recent days. In this paper, the results of residualbased a posteriori error estimators, which evaluate the discretization error in the finiteelement computation, are extended to the case of several kinds of source terms for both A/φ and T/Ω harmonic formulations. The definitions of the estimators are given and some numerical examples are provided to show the behavior of the estimators. 
[9] 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 
[10] Finite element mesh adaptation strategies from residual and hierarchical error estimators in eddy current problems IEEE Transactions on Magnetics, Vol. 51, N°. 3, 04/2015, URL, Abstract DULAR Patrick, LE MENACH Yvonnick, TANG Zuqi, CREUSE Emmanuel, PIRIOU Francis 
A strategy of mesh adaptation in eddy current finite element modeling is developed from both residual and hierarchical error estimators. Wished distributions of element sizes of adapted meshes are determined from the elementwise local contributions to the estimators and define constraints for the mesh generator. Uniform distributions of the local error are searched. 
[11] Spacetime residualbased a posteriori estimator for the Αφ formulation in eddy current problems. Magnetics, IEEE Transactions, Vol. 51, N°. 3, 03/2015, Abstract TITTARELLI Roberta, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis, MOREAU Olivier, BOITEAU Olivier 
In this work, an a posteriori residual error estimator is presented for the 3D eddy current problem modeled by the spacetime Aphi potential formulation. It is solved by the finite element method in space and the backward Euler scheme in time. Once the reliability as well as the efficiency of the estimator are established, two numerical tests are proposed: an analytical one in order to validate the theoretical results and a physical one in order to illustrate the performance for a real eddy current problem. 
[12] 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.

[13] Comparison of Residual and Hierarchical Finite Element Error Estimators in Eddy Current Problems IEEE Transactions on Magnetics, Vol. 50, N°. 2, pages. 501504, 02/2014, URL, Abstract DULAR Patrick, TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, PIRIOU Francis 
The finite element computation of eddy current problems introduces numerical error. This error can only be estimated. Among all error estimators (EEs) already developed, two estimators, called residual and hierarchical EEs, proven to be reliable and efficient, are theoretically and numerically compared. Both estimators show similar behaviors and locations of the error. 
[14] Residual and equilibrated error estimators for magnetostatic problems solved by finite element method IEEE Transactions on Magnetics, Vol. 49, N°. 12, pages. 5715  5723, 12/2013, URL, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis 
In finite element computations, the choice of the mesh is crucial to obtain accurate solutions. In order to evaluate the quality of the mesh, a posteriori error estimators can be used. In this paper, we develop residualbased error estimators for magnetostatic problems with both classical formulations in term of potentials used, as well as the equilibrated error estimator. We compare their behaviors on some numerical applications, to understand the interest of each of them in the remeshing process. 
[15] 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. 
[16] A posteriori error estimator for harmonic APhi formulation The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32, N°. 4, pages. 1219  1229, 07/2013, URL TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis 
[17] Residual based a posteriori error estimators for harmonic A/Phi and T/Omega formulations in eddy current problems IEEE Transactions on Magnetics, Vol. 49, N°. 5, 05/2013, URL TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis 
[18] 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. 
[19] Residualbased a posteriori estimators for the T/Omega magnetodynamic harmonic formulation of the Maxwell system International Journal of Numerical Analysis and Modeling, Vol. 10, N°. 2, pages. 411429, 02/2013, URL, Abstract CREUSE Emmanuel, NICAISE Serge, TANG Zuqi, LE MENACH Yvonnick, NEMITZ Nicolas, PIRIOU Francis 
In this paper, we focus on an a posteriori residualbased error estimator for the T/Omega
magnetodynamic harmonic formulation of the Maxwell system. Similarly to the A/Phi formulation, the weak continuous and discrete formulations are established, and the wellposedness of
both of them is addressed. Some useful analytical tools are derived. Among them, an adhoc
Helmholtz decomposition for the T/Omega
case is derived, which allows to pertinently split the error.
Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally
efficient. Finally, numerical tests confirm the theoretical results. 
[20] 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). 
[21] Residualbased a posteriori estimators for the A/Phi magnetodynamic harmonic formulation of the Maxwell system Mathematical Models and Methods in Applied Sciences, Vol. 22, N°. 5, pages. 30, 05/2012, URL, Abstract CREUSE Emmanuel, NICAISE Serge, TANG Zuqi, LE MENACH Yvonnick, NEMITZ Nicolas, PIRIOU Francis 
This paper is devoted to the derivation of an a posteriori residualbased error estimator for the APhi magnetodynamic harmonic formulation of the Maxwell system. The weak continuous and discrete formulations are established, and the wellposedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad hoc Helmholtz decomposition is proven, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results. 
[22] 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 
[23] 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 
[24] Parallel direct solver for the finite integration technique in electrokinetic problem IEEE Trans mag, Vol. 46, N°. 8, pages. 32693272, 08/2010 TINZEFTE Abdellatif, LE MENACH Yvonnick, KORECKI Julien, GUYOMARC’H Frédéric, PIRIOU Francis 
[25] 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. 
[26] Hysteresis Phenomenon Implementation in FIT: Validation with Measurements IEEE Transactions on Magnetics, Vol. 46, N°. 8, pages. 32853288, 08/2010, URL, Abstract KORECKI Julien, BENABOU Abdelkader, LE MENACH Yvonnick, DUCREUX JeanPierre, PIRIOU Francis 
The presented work is about the implementation of a vector hysteresis model in a Finite Integration Technique (FIT) calculation code. This is achieved in the magnetostatic case using the vector potential formulation and with the external electric circuit coupling. The used behavior law model is the vectorized JilesAtherton model with the magnetic flux density as input variable. The proposed approach is illustrated by modeling a coil made of Soft Magnetic Composite (SMC) magnetic core. Comparison with measured global quantities is also performed. 
[27] Parallel direct solver for the finite integration technique in electromagnetics COMPEL, Vol. 29, N°. 4, pages. 941949, 07/2010 TINZEFTE Abdellatif, LE MENACH Yvonnick, KORECKI Julien, PIRIOU Francis 
[28] 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. 
[29] 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 
[30] Accurate Projection Method of Source Quantities in Coupled FiniteElement Problems IEEE Transactions on Magnetics, Vol. 45, N°. 3, pages. 11321135, 03/2009, Abstract PARENT Guillaume, DULAR Patrick, PIRIOU Francis, ABAKAR Ali 
Projecting discrete quantities from one mesh to another one is a critical operation which is usually required in multiphysical
problems. The efficiency of a Galerkin projection method is studied for magnetothermal and magnetoelasticity couplings. As examples
of application, two electromagnetic devices are studied: a threephase busbar system as a magnetothermal problem and an electromagnet
as a magnetomechanical problem. 
[31] Iterative Solvers For Singular Symmetric Linear Systems in Electromagnetism Low Frequency IEEE Trans Mag, Vol. 45, N°. 3, pages. 1428  1431, 03/2009 TINZEFTE Abdellatif, LE MENACH Yvonnick, PIRIOU Francis 
[32] Method to Connect NonConforming Mesh in 3D with the Overlapping Method IEEE transactions on Magnetics, Vol. 45, N°. 3, pages. 14201423, 03/2009 KREBS Guillaume, CLENET Stéphane, ABAKAR Ali, LOCMENT Fabrice, PIRIOU Francis 
[33] Implementation of an Anisotropic Vector Hysteresis Model In a 3D Finite Element Code IEEE Transactions on Magnetics, Vol. 44, N°. 6, pages. 918921, 06/2008, Abstract LEITE Jean Vianei, BENABOU Abdelkader, SADOWSKI Nelson, CLENET Stéphane, BASTOS João Pedro Assumpção, PIRIOU Francis 
Abstract  The implementation of a vector hysteresis model in 3D finite element (FE) magnetic field calculation is performed. The vector model is derived from the original scalar JilesAtherton one. The hysteresis model has been implemented in a 3D vector potential formulation. The nonlinear equation system is solved by the NewtonRaphson method. 
[34] Comparison between the Mortar Element Method and the polynomial Interpolation Method to model movement in the Finite Element Method IEEE, Vol. 44, N°. 6, pages. 1311317, 06/2008 SHI Xiaodong, LE MENACH Yvonnick, DUCREUX JeanPierre, PIRIOU Francis 
[35] 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 
[36] Using Galerking Projection Method in MagnetoThermal Coupled Problems IEEE Trans. Mag., 04/2008, Abstract PARENT Guillaume, DULAR Patrick, DUCREUX JeanPierre, PIRIOU Francis 
In term of magnetothermal coupling, two different strategies � direct and indirect � can be used. One of the advantages of the indirect coupling strategy is its ability to solve each problem separately on dedicated meshes. However, such a technique requires a projection of each solution obtained on one mesh onto another one. In this paper a comparison of two projection methods � collocation and Galerkin projection method  is presented. 
[37] Design of a permanent magnet actuator for linear and rotary movements European Physical Journal ("Applied physics"), 04/2008, Abstract KREBS Guillaume, TOUNZI Abdelmounaïm, PAUWELS Brecht, WILLEMOT Dirk, PIRIOU Francis 
We describe in this paper the design of a permanent magnet actuator for linear and rotary movement. The actuator can make linear and rotary movements and special attention has been placed on the simplicity and the swiftness behavior. At first, we compare the different approaches to perform a linked movement and a structure is adopted. Then, we detail the adopted magnetic conversion through a rotary machine and a linear actuator. In a last part, the studied actuator is presented and results concerning the flux linkages and forces are given using 3D finite element simulations. 
[38] Numerical solutions in primal and dual mesh of magnetostatic problem
solved with the Finite Integration Technique
COMPEL, Vol. 27, N°. 1, pages. 4755, 01/2008, Abstract KORECKI Julien, LE MENACH Yvonnick, DUCREUX JeanPierre, PIRIOU Francis 
A paraître Abstract  To solve the Maxwell’s equations in the magnetosatic case the formulations in terms of vector potential or scalar potential can be used. If to solve the equations we use the Finite Element Method on the primal mesh we obtain two complementary solutions. In this paper, both formulations in terms of potential and using the fields H and B are developed and solved with the help of the Finite Integration Technique. The solutions computed in the primal and dual meshes are analysed and discussed. 
[39] 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. 
[40] 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 
[41] 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. 
[42] Design and study of a linear actuator using an analytical approach and the 3D FEM
COMPEL, Vol. 26, N°. 4, pages. 102116, 01/2007, Abstract KREBS Guillaume, TOUNZI Abdelmounaïm, PAUWELS Brecht, WILLEMOT Dirk, PIRIOU Francis 
Nowadays, the electromagnetic actuators for industrial processes have to present very specific features which can not always be obtained by classical machines. Hence, to reach the wanted features, one has to design the actuator and to quantify its performance with a good accuracy and reasonable computation time. The purpose of this paper is to present the design and the study of a linear actuator. First, we present the design of the chosen actuator structure. The second part is devoted to describe the approaches used (permeance network model and the 3D Finite element model) to study the behaviour of the actuator. Lastly, we give the results of the study, obtained by both models, and we compare them to experimental data obtained from the prototype build up.

[43] Study of a stator current excited vernier reluctance machine IEEE Energy Conversion, Vol. 21, N°. 4, pages. 823831, 12/2006 TAÏBI Soufiane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[44] Application of FiniteElement Method to a PMLSM with NonSinusoidal Electromotive Force Transactions on Industrial Application of IEE, Japan, Vol. 126, N°. 10, pages. 13571362, 10/2006, URL, Abstract REMY Ghislain, TOUNZI Abdelmounaïm, BARRE PierreJean, PIRIOU Francis, HAUTIER JeanPaul 
An accurate thrust control of permanent magnet linear synchronous motors (PMLSM) is more efficient with a fine knowledge
of the harmonics value of the electromotive force (EMF). This is often difficult to obtain experimentally for a PMLSM. As a
consequence, this paper deals with the study of the nonsinusoidal EMF of a PMLSM using the 3D FiniteElement Method
(FEM). Two potential formulations are used to consider several cases. Afterwards, for the same accuracy, the computation times
are examined. The results of the FEM are compared to those given by the measurements from a test bench composed of a
Siemens LIMES400/120 linear motor and a dSPACE DS1005 realtime controller board. Finally, the advantages and the
limitations of the FE Analysis will be discussed. 
[45] Design and Study of a Multiphase Axialflux machine IEEE Transaction on Magnetics, Vol. 42, N°. 4, pages. 14271430, 04/2006, URL, Abstract LOCMENT Fabrice, SEMAIL Eric, PIRIOU Francis 
In this paper, a 7phase Axialflux Doublerotor Permanent Magnet Synchronous Machine is studied using analytical and Finite Element methods. This type of machine shows a higher sensitivity to the inductance harmonics and electromotive force (emf) compared with the 3phase machines. So, the conventional analytical modeling method, in which only the first harmonic is taken into account, leads to significant errors in the determination of the control parameters, e.g. the frequency of Pulse Width Modulation Voltage Source Inverter. A multimachine model explains the reasons for this sensitivity and a more sophisticated analytical method is used. Results are compared with those obtained by the 3D FEM. 
[46] 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 
[47] Determination of magnetic characteristics of a variable reluctance machine excited by DC and AC currents COMPEL, Vol. 25, N°. 1, pages. 102116, 03/2006 TAÏBI Soufiane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[48] COMPARISON OF SLIP SURFACE AND MOVING BAND TECHNIQUES FOR MODELLING MOVEMENT IN 3D WITH FEM COMPEL, Vol. 25, N°. 1, pages. 1730, 01/2006, Abstract SHI Xiaodong, LE MENACH Yvonnick, DUCREUX JeanPierre, PIRIOU Francis 
In this paper the slip surface and the moving band techniques are used to model the rotation of electrical machines in 3D with FEM and the results are compared. For the slip surface technique, several method are explained; such as the lockedstep approach and linear and quadratic interpolation. For this study, the proposed techniques are applied to a permanent magnet synchronous machine. The comparison is carried out at noload for the electromotive force and the cogging torque. Furthermore, the torque is also compared for the shortcircuit case. 
[49] Consideration of the coupling of the magnetic and electric equations with Finite Integration Technique (FIT)
European Physical Journal Applied Physics, Vol. 30, N°. 1, pages. 1721, 04/2005, Abstract ALBERTIER Grégory, LE MENACH Yvonnick, DUCREUX JeanPierre, PIRIOU Francis 
In this paper, the Finite Integration Technique and an approach to solve simultaneously the magnetic and electric circuit equations is presented in magnetostatic case. The developments of the FIT will be compared with those used for the Finite Element Method. As example of application an iron core coil is studied and the results of both approaches are compared 
[50] 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 
[51] Comparison of the Preisach and JilesAtherton models to take hysteresis phenomenon into account in Finite Element Analysis The international Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), Vol. 23, N°. 3, pages. 825  834, 09/2004, URL, Abstract BENABOU Abdelkader, CLENET Stéphane, PIRIOU Francis 
Résumé  In this communication, the Preisach and JilesAtherton models are studied to take hysteresis phenomenon into account in finite element analysis. First, the models and their identification procedure are briefly developed. Then, their implementation in the finite element code is presented. Finally, their performances are compared with an electromagnetic system made of soft magnetic composite. Current and iron losses are calculated and compared with the experimental results. 
[52] Adaptation of the Frequency Dependent JilesAtherton Model with B as entry variable International Journal of Applied Electromagnetics and Mechanics, Vol. 19, N°. 14, pages. 187  191, 06/2004, URL, Abstract BENABOU Abdelkader, CLENET Stéphane, PIRIOU Francis 
Résumé  In this communication, we propose a dynamical model of hysteresis giving the magnetization M in function of the flux density B. The mathematical development is based on the Jiles approach for frequency dependent hysteresis. The obtained model is simple to carry out and fast. The model is tested through a comparison with experimental results on FeSi steel sheets. Then, the accuracy and the range of application of the model are discussed. 
[53] 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 
[54] 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 
[55] 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 
[56] Machines à réluctance Vernier : Conditions de fonctionnement RIGE, Vol. 6, N°. 56, pages. 637664, 10/2003 TAÏBI Soufiane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[57] Comparison of Preisach and Jiles–Atherton models to take into account hysteresis phenomenon for finite element analysis Journal of Magnetism and Magnetic Materials, Vol. 261, N°. 12, pages. 139160, 04/2003, URL, Abstract BENABOU Abdelkader, CLENET Stéphane, PIRIOU Francis 
Résumé  In electrical engineering, study and design of electromagnetic systems require more and more accurate models. To improve the accuracy of field calculation code, hysteresis phenomenon has to be taken into account to model ferromagnetic material. This material model has to be accurate and fast. In that context, two macroscopic models are often used: the Preisach and the Jiles–Atherton (J–A) models.
In this paper, both models are presented. Field calculation requires a model giving the magnetization M versus either the magnetic field H or the magnetic flux density B. Consequently, from the classical Preisach and J–A, two submodels M(H) and M(B) are deduced. Then, we aim at comparing these models in terms of identification procedure facilities, accuracy, numerical implementation and computational effort. This study is carried out for three kinds of materials, which have different magnetic features: ferrites, FeSi sheets and a soft magnetic composite material. Then, the implementation of these models in a finite element code is presented. As example of application, a highfrequency transformer supplied by a rectangular voltage is studied. 
[58] A non linear analytical model of switched reluctance machines European Physical Journal  Applied Physics, pages. 163172, 07/2002 SOFIANE Yamina, TOUNZI Abdelmounaïm, PIRIOU Francis 
[59] Study of Head Winding Effects in a Switched Reluctance Machine IEEE Trans Mag, Vol. 38, N°. 2, pages. 989992, 03/2002 SOFIANE Yamina, TOUNZI Abdelmounaïm, PIRIOU Francis, LIESE Manfred 
[60] Determination of the local distribution of magnetics losses for the optimal design of transformers COMPEL, Vol. 20, N°. 1, pages. 187204, 01/2002 CLENET Stéphane, CROS Jérôme, VIAROUGE Philippe, PIRIOU Francis, LEFEVRE Louis Philippe 
[61] Design and study of a double air gap Excited Vernier Reluctance Machine Studies in Applied Electromagnetics and Mechanics, Vol. 22, pages. 305310, 01/2002 TAÏBI Soufiane, TOUNZI Abdelmounaïm, CLENET Stéphane, PIRIOU Francis 
[62] The use of Genetic Algorithm to reduce the torque ripples of a Vernier Reluctance Machine Studies in Applied Electromagnetics and Mechanics, Vol. 22, pages. 311316, 01/2002 TAÏBI Soufiane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[63] Numerical model to discretize source fields in the 3D finite elements method IEEE Transactions Magnetics, Vol. 36, N°. 4, pages. 676679, 07/2000, Abstract LE MENACH Yvonnick, CLENET Stéphane, PIRIOU Francis 
This communication presents a method to discretize electromagnetic source fields in the Whitney element spaces for static electromagnetic potential formulations. This method requires no finite element solution to calculate this source fields. It is based on the use of a facet or an edge tree. We will test it on electrokinetic, electrostatic and magnetostatic examples 
[64] Error Estimators in 3D Linear Magnetostatics IEEE transactions on Magnetics, Vol. 36, N°. 4, pages. 15861591, 04/2000 MARQUES Georges, CLENET Stéphane, PIRIOU Francis 
[65] Calculation of Complementary Solution in 2D Finite Element Method: Application to Error Estimation IEEE Transaction on Magnetics, Vol. 36, N°. 4, pages. 15831587, 04/2000 MARMIN Fabienne, CLENET Stéphane, BOUILLAULT Frédéric, PIRIOU Francis 
[66] Adaptive meshing in 3D multistatic problem with variable sources European Phycal Journal  Applied Physics, Vol. 12, N°. 3, pages. 187193, 03/2000 MARQUES Georges, CLENET Stéphane, PIRIOU Francis 
[67] 3D computation of a claw pole magnet machine using a scalar potential formulation European Physical Journal Applied Physics, Vol. 12, N°. 3, pages. 175182, 01/2000, Abstract LE MENACH Yvonnick, CLENET Stéphane, PIRIOU Francis, LETOURNEAU JeanFrançois, VIAROUGE Philippe 
In this paper, a claw pole permanent magnet machine is studied using a 3D scalar potential formulation. First, the discretization of Maxwell’s equations using Whitney’s elements is presented. Especially, the method to take the winding current distribution into account by means of source fields is detailed. Then, a numerical model of the studied machine is presented. Simulation results (inductance, EMF, torque) are discussed by comparison with experimental ones.

[68] 3D compatible magnetostatic potential formulations coupled with electrical circuits
COMPEL, Vol. 13, N°. 3, pages. 776786, 01/2000, Abstract LE MENACH Yvonnick, CLENET Stéphane, PIRIOU Francis 
This paper presents a method of coupling magnetostatic potential formulations with electrical circuits for the 3D FEM. Allowing for the current density distribution in stranded conductors, two vectors N and K are introduced. A systematic method of decomposing both vectors in Whitney’s element spaces is suggested. This method can be used for coils with a complex shape. As an example of application a threephase transformer is studied.

[69] Numerical Modelling of an Unbalanced Short Shunt Induction Generator using Finite Element Method COMPEL, Vol. 19, N°. 3, pages. 787804, 01/2000 BRULE Stéphane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[70] Coupling of magnetic and electrical circuit equations using coil shape functions International Journal of Theorical Electrotechnics, pages. 3639, 03/1999, Abstract LE MENACH Yvonnick, CLENET Stéphane, PIRIOU Francis 
In this paper we propose, an approach for coupling magnetostatic and electric circuit equations applicable to the case of stranded conductors. The method based on the calculation of global quantities is presented and applied to the magnetic formulation HsƒÇ. The properties and calculation of source field Hs are also discussed. As an example we have studied a permanent magnet synchronous machine. At no load, the magnetomotive force is determined and compared with experimental results. A calculation when the generator has a resistance load is also presented 
[71] Determination and utilization of the source field in 3D magnetostatic problems IEEE Transactions Magnetics, Vol. 34, N°. 5, pages. 25092512, 09/1998, Abstract LE MENACH Yvonnick, CLENET Stéphane, PIRIOU Francis 
In this paper we study different approaches to introduce the source terms due to the inductors crossed by a uniform current density J 0 in 3D FEM. Two equivalent methods are developed to decompose the current density J in the facet element space with divergence free close to J0. This decomposition is used in the aformulation without gauge condition. Moreover, from the flux facet the source field Hs can be calculated in the edge element space and introduced into the öformulation. As examples of applications we have studied a coil with a complex geometry and a iron core coil 
[72] Error Estimation on Finite Element Solution in Non Linear Magnetostatic 2D Problems IEEE Transactions on Magnetics, Vol. 34, N°. 5, pages. 32683271, 09/1998 MARMIN Fabienne, CLENET Stéphane, PIRIOU Francis, BUSSY Pascal 
[73] Design and optimisation of an excited reluctance generator using field computation IEEE Trans Mag, pages. 34943497, 09/1998 HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
[74] Error estimator in 2D linear magnetostatic European Physical Journal of Applied Physics, Vol. 1, pages. 203209, 01/1998 MARMIN Fabienne, CLENET Stéphane, BUSSY Pascal, PIRIOU Francis 
[75] Characterization and modelling of hysteresis phenomenon Mathematics and Computers in Simulation, Vol. 4, N°. 34, pages. 301336, 01/1998 DEBRUYNE Herve, CLENET Stéphane, PIRIOU Francis 
ACLN Revue nationale avec comité de lecture 
[1] Introduction des grandeurs globales dans les problèmes d’électrocinétique résolus avec la F.E.M. et la F.I.T. RIGE, Vol. 11, N°. 23, pages. 185203, 04/2008, Abstract KORECKI Julien, LE MENACH Yvonnick, VERITE JeanClaude, PIRIOU Francis 
Cette communication présente une approche permettant d’imposer le courant ou la différence de potentiel dans le cas d’un problème d’électrocinétique. Pour une formulation en potentiel vecteur, l’approche proposée a été implantée dans un code de calcul basé sur la Technique d’Intégration Finie et dans un code éléments finis. Des simulations sont réalisées pour des cas simples et les résultats sont comparés à ceux obtenus à l’aide de la méthode des éléments finis. 
[2] Modélisation de cycle d’hystérésis RIGE, Vol. 5, N°. 2, pages. 359369, 04/2002 BERNARD Yves, CLENET Stéphane, OULED AMOR A, BOUILLAULT Frédéric, PIRIOU Francis 
[3] Production d’énergie décentralisée par un système Machine à Réluctance VariableConvertisseurs statiques REE, pages. 4955, 07/1998 HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
ACT Conférence internationale avec acte 
[1] Canal Lock Variable Speed Hydropower Turbine Energy Conversion System EVER 2017, 04/2017 ZHANG Jian, TOUNZI Abdelmounaïm, DELARUE Philippe, PIRIOU Francis, LEONTIDIS Vlasios, DAZIN Antoine, CAIGNAERT Guy, LIBAUX Antoine 
[2] Quantitative design of a high performance permanent magnet vernier generator Intermag 2017, 04/2017 ZHANG Jian, TOUNZI Abdelmounaïm, LEONTIDIS Vlasios, DELARUE Philippe, PIRIOU Francis, CAIGNAERT Guy, LIBAUX Antoine, DAZIN Antoine 
[3] 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 
[4] Lock hydroelectrical power generation feasability study ViennaHydro, Vienne, 11/2016 LEONTIDIS Vlasios, ZHANG Jian, CAIGNAERT Guy, DELARUE Philippe, TOUNZI Abdelmounaïm, PIRIOU Francis, LIBAUX Antoine, DAZIN Antoine 
[5] 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. 
[6] 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 
[7] 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. 
[8] 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 
[9] 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. 
[10] Comparison of Residual and Hierarchical Finite Element Error
Estimators in Eddy Current Problems COMPUMAG 2013 Budapest, Hungary, 07/2013, URL, Abstract TANG Zuqi, DULAR Patrick, LE MENACH Yvonnick, CREUSE Emmanuel, PIRIOU Francis 
The finite element computation of eddy current
problems gives numerical error. This error cannot be calculated,
but can only be estimated. Among all error estimators already
developed, it is proposed to compare two proven estimators
called residual and hierarchical error estimators. 
[11] Improving the quality of computational phantoms by using a surface subdivision method: effect on the computational results BioEM2013, Thessaloniki, Greece, 06/2013 LELONG Thomas, THOMAS Pierre, SCORRETTI Riccardo, PIRIOU Francis, MAGNE I 
[12] 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.

[13] Improving the mesh quality of
computational phantoms EMF, 2013, Brugge, 04/2013 LELONG Thomas, THOMAS Pierre, SCORRETTI Riccardo, PIRIOU Francis, BUAIS N 
[14] Residual based a posteriori error estimator for harmonic APhi and TOmega formulation in eddy current problems CEFC 2012 Oita, Japan, 11/2012, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis 
For the eddy current problem, the potential formulations are widely used today. In this communication, residual based a posteriori error estimators are introduced to evaluate the discretization error in the finite element calculation in both case of APhi and TOmega harmonic formulations. An example is carried out to show the behavior of our estimators. 
[15] A posteriori error estimator for harmonic APhi formulation EPNC 2012 Pula, Croatia, 06/2012, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis 
In this paper a residualbased error estimator is proposed to evaluate the numerical error induced by the computation of the electromagnetic systems using a Finite Element Method in the case of the harmonic APhi formulation. This estimator is based on the evaluation of quantities weakly verified by the formulation. Furthermore as this estimator verifies the notions of reliability and efficiency it allows to estimate the qualities of local and global solutions. Two examples of electromagnetic systems with current density induced are used to show the efficiency of the proposed estimator. 
[16] 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). 
[17] 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. 
[18] Comparison of Residual and Equilibrated Error Estimators for FEM Applied to Magnetostatic Problems COMPUMAG 2011 Sydney, Australie, 07/2011, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis 
In finite element computations, the choice of the mesh is crucial to obtain an accurate solution. In order to evaluate
the quality of the mesh, a posteriori error estimators can be used. In this paper, we analyze and compare the residual and equilibrated error estimators for magnetostatic problems. 
[19] Reduction of force ripples in PM planar actuator ICEM 2010  International Conference on Electrical Machines, Rome, Italy, 92010, 09/2010 KREBS Guillaume, TOUNZI Abdelmounaïm, PIRIOU Francis, PAUWELS Brecht, WILLEMOT Dirk 
[20] 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. 
[21] Preconditioner for Mortar method applied to the FEM CEFC 2010, 05/2010 TINZEFTE Abdellatif, AUBERTIN Mathieu, HENNERON Thomas, PIRIOU Francis 
[22] 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 
[23] 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. 
[24] Parallel Direct Solver For The Finite Integration Technique in Electrokinetic Problems Compumag 2009, florianopolis, brésil, 11/2009 TINZEFTE Abdellatif, LE MENACH Yvonnick, KORECKI Julien, PIRIOU Francis, GUYOMARC’H Frédéric 
[25] 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 
[26] Parallel direct solver for the finite integration
TECHNIQUE IN ELECTROMAGNETICS ISEF 2009 Arras France, 10/2009, Abstract TINZEFTE Abdellatif, LE MENACH Yvonnick, KORECKI Julien, PIRIOU Francis 
The Finite Integration Technique is used in the different engineering domains as well as to computing the electromagnetic phenomena. This technique is efficient if the mesh is generated by
hexahedron elements. Moreover the matrix system, obtains from a regular mesh, can be exploit to use the parallel direct solver. In fact, in reordering the unknowns by the nested dissection method, it is possible to
construct directly the lower triangular matrix of the Cholesky factorization with many processors without
assembling the matrix system. In this paper, the parallel direct solver is described and the efficiency is shown as function to the number of processors. 
[27] 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 
[28] 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 
[29] Accounting for linear movement in 3D FEM using the overlapping method accepted to be presented at EPNC 2008, 07/2008, Abstract KREBS Guillaume, CLENET Stéphane, ABAKAR Ali, TOUNZI Abdelmounaïm, PIRIOU Francis 
In this paper, movement strategy, using the overlapping method, is studied. Nonconforming tetrahedral meshes and planar displacements are considered. The first part of this paper is devoted to the presentation of the FEM formulation. In the second part, the overlapping method is described in the case of planar movements. At last, results are given and discussed. 
[30] Analysis of dual formulations for eddy current problems with FIT EPNC 2008, 07/2008, Abstract KORECKI Julien, LE MENACH Yvonnick, PIRIOU Francis, DUCREUX JeanPierre 
This paper presents a method allowing to impose global electrics quantities, in a time step magnetodynamic case, simulated with the Finite Integration Technique. The A and TΩ formulations are developed and two vectors fields are associated in order to impose and compute global quantities, such as currents and voltages. Several simulations, applied to a system with two conductors, were carried out and the results were compared to those obtained with the finite element method. 
[31] 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 
[32] Insulating layers in electrokinetics problem solved by the FEM ACOMEN 2008 (Liege), 05/2008 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
[33] Iterative Solvers For Singular Symmetric Linear
Systems in Electromagnetism Low Frequency Conference CEFC 08 Athens, 05/2008, Abstract TINZEFTE Abdellatif, LE MENACH Yvonnick, PIRIOU Francis 
Application of different iterative methods (CG,MRTR, SQMR, MINRES) are proposed to solve linear systems from Finite Element Method (FEM) in 3D electromagnetic field analysis, and their convergences are compared. 
[34] Method to connect nonconforming mesh in 3D with the overlapping method CEFC 2008, 05/2008, Abstract KREBS Guillaume, CLENET Stéphane, LE MENACH Yvonnick, LOCMENT Fabrice, PIRIOU Francis 
In this paper, the overlapping method is applied to connect nonconforming tetrahedral meshes. At first the FEM formulation is described. The overlapping method is presented as well as its implementation in a FEM calculation code. At last, applications will be studied and discussed. 
[35] Modeling of a linear and rotative permanent magnet actuator Intermag 2008, Madrid, Espagne, 01/2008 KREBS Guillaume, TOUNZI Abdelmounaïm, PAUWELS Brecht, WILLEMOT Dirk, PIRIOU Francis 
[36] Control of a PM linear actuator using Hall effect sensors LDIA 2007, 6th International Symposium on Linear Drives for Industrial Applications, 09/2007, Abstract KREBS Guillaume, TOUNZI Abdelmounaïm, PAUWELS Brecht, WILLEMOT Dirk, PIRIOU Francis 
Due to industrial needs, small stroke actuators present a growing interest. Generally, high acceleration, robustness and low manufacturing costs are frequently required. Today, improvements in the magnetic material as rare earth magnets or iron powder permit to design very compact actuators.
To reach high performances, the actuator has to be controlled. This can be achieved using the last control capabilities (dsp, fpga...).However, this often needs sensors which increase the costs.
In this paper, we deal with the simulation of the control of a PM linear small stroke actuator with non mechanical sensors. First, we present the actuator features. Then we introduce the simulation model based on the reluctance network model. To reach the information related to the position of the moving part, we use Hall effect sensors. In a third part, we show the placements of the sensors. Lastly, we introduce the control strategy and give some simulation results.

[37] Implementation of an Anisotropic Vector Hysteresis Model In a 3D Finite Element Code Compumag 2007, Aachen, Germany, 07/2007 LEITE Jean Vianei, BENABOU Abdelkader, SADOWSKI Nelson, CLENET Stéphane, BASTOS João Pedro Assumpção, PIRIOU Francis 
[38] Study of Magnetic Induction Measurement Techniques in Rotational Single Sheet Tester Compumag 2007, Aachen, 06/2007 DA SILVA Pedro Armando, SADOWSKI Nelson, BENABOU Abdelkader, BATISTELA N.J., BASTOS João Pedro Assumpção, CLENET Stéphane, PIRIOU Francis 
[39] Calcul de flux magnétique locaux avec la méthode des éléments finis NUMELEC’06, 11/2006 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
[40] Soft Magnetic Composite Axial flux sevenphase machine ICEM 2006, 09/2006, Abstract LOCMENT Fabrice, SEMAIL Eric, PIRIOU Francis 
A faulttolerant sevenphase axialflux permanent magnet (AFPM) machine with a soft magnetic composite (SMC) stator has been designed thanks to analytical and 3D finite element method. In this paper, we present its characteristics and show that a high number of phases allows to get a good quality of the torque with a design simpler than this one of the threephase AFPM machines. Experimental backelectromotive forces (backEMF) and the cogging torque are then compared with predeterminations. Finally, experimental torque of a drive composed of a sevenleg Voltage Source Inverter (VSI) supplying the machine in a vector control is presented. 
[41] Two cogging force minimization applied to a linear actuator ICEM06, 09/2006, Abstract KREBS Guillaume, TOUNZI Abdelmounaïm, PAUWELS Brecht, WILLEMOT Dirk, PIRIOU Francis 
Permanent magnet actuators, widely used, often suffer from torque or force ripples. In this paper, we intend to reduce the cogging
force of a PM linear actuator using two approaches. The first one consists on an optimisation of the teeth and magnet sizes. The
second deals with the use of a supplementary steel piece in order create an opposite cogging force. The first calculations are achieved
using 2DFEM. Then 3DFEM is used to validate the results. 
[42] 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. 
[43] A hybrid movement method to model electrical machines with end winding in 3D Finite Element Method CEFC, 06/2006, Abstract SHI Xiaodong, LE MENACH Yvonnick, ABAKAR Ali, DUCREUX JeanPierre, PIRIOU Francis 
In this paper, a hybrid method is proposed for the simulation of rotating electrical machines taking into account the end winding effect. The method is based on the sliding surface that is decomposed on two parts. In the air gap we use the interpolation method at the second order and in the area of the end winding the Surface Interpolation Method (first order). As application a turbogenerator is studied. 
[44] Design and study of a linear actuator using the 3D FEM EPNC06, 06/2006, Abstract KREBS Guillaume, TOUNZI Abdelmounaïm, PAUWELS Brecht, WILLEMOT Dirk, PIRIOU Francis 
The electromagnetic actuators for industrial processes have nowadays to present very specific features. To lead to a
prototype and to study it with high accuracy, we use today partially or completely numerical methods. The purpose of
this paper is to present the design and the study of a linear actuator. First, we present the structure of the actuator
and its characteristics. The second part is devoted to describe the numerical approach. Lastly, we give the main results
of the study and compare them to experimental data obtained from a prototype. 
[45] A locked step procedure to take into account two different movements in the 3DFEM EMF06, 06/2006, Abstract KREBS Guillaume, TOUNZI Abdelmounaïm, PAUWELS Brecht, WILLEMOT Dirk, PIRIOU Francis 
In the field of numerical modeling, applications with complex displacements are more and more met. The present paper deals
with a procedure which permits to take into account two movements in the finite element method. Using the locked step method,
it is possible perform both XY and Xq displacements. The procedure developed is explained and a 3D simple example is studied,
both in magnetostatic and magnetodynamic, to show the validity of the proposed method. 
[46] Study of the coupling between magnetic and electric equations
by using FEM, FIT and Cellmethod EPNC 2006, Maribor (Slovenia), 06/2006, URL, Abstract PARENT Guillaume, LE MENACH Yvonnick, DUCREUX JeanPierre, PIRIOU Francis 
Usually the Finite Element Method (F.E.M) is used to model the electromagnetic devices for low frequency. But other methods can be used as the CellMethod and the Finite Integration Technique (F.I.T.). The presented work is a comparative study about these methods. Their theories are reminded to show that the same source field can be used for all methods. The properties of the mass matrices generated though the three different methods are also discussed. Finally, as an example of application an iron core coil supplied by a voltage source is modelled. 
[47] 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. 
[48] Influence of Source Fields on FEM Potential Formulations in Magnetostatics CEFC 2006, 03/2006 HENNERON Thomas, CLENET Stéphane, BASTOS João Pedro Assumpção, PIRIOU Francis 
[49] Calculation of global quantities using incidence matrix in the Aφ formulation CEM 2006, 02/2006 HENNERON Thomas, CLENET Stéphane, PIRIOU Francis 
[50] FiniteElement Analysis of NonSinusoidal Electromotive Force in a Permanent Magnet Linear Synchronous Motor LDIA 2005, The 5th International Symposium on Linear Drives for Industry Applications, Awaji Yumebutai, Hyogo, Japan, 09/2005, Abstract REMY Ghislain, TOUNZI Abdelmounaïm, BARRE PierreJean, PIRIOU Francis, HAUTIER JeanPaul 
In the case of permanent magnet linear synchronous motors (PMLSM), knowledge of the electromotive force (emf) is necessary to achieve accurate control. However, it is often difficult to obtain it experimentally. As a consequence, this paper deals with the study of the nonsinusoidal emf of a PMLSM using the FiniteElement Method (FEM). Two potential formulations are used to consider several cases. Then, for the same accuracy, the computation times are compared. The results of the FEM are compared to those given by the measurements from a test bench composed of a Siemens LIMES400/120 linear motor and of a dSPACE DS1005 realtime controller board. Finally, the effectiveness and the limits of the FE Analysis will be discussed. 
[51] Comparison of Methods to Simulate the Movement of Electrical Machines in 3D Using FEM COMPUMAG, Vol. 3, pages. 80, 06/2005, Abstract SHI Xiaodong, LE MENACH Yvonnick, DUCREUX JeanPierre, PIRIOU Francis 
In this paper three techniques ( the lockedstep approach, the overlapping method and the nodal interpolation method) are compared to model the rotation of electrical machines in 3D using FEM. These methods are associated with a formulation expressed in terms of scalar potential. To extend the possibilities of the interpolation method we propose the Surface Interpolation Method, which allows us to use nonconform meshes in the air gap of the studied machine. These different techniques are used to model a permanent magnet machine and a turbogenerator. The results obtained are compared by calculating the electromotive force and the torque. 
[52] COMPARISON OF DIFFERENT TECHNIQUES TO MODEL THE MOVEMENT IN 3D WITH FEM EPNC, 12/2004, Abstract SHI Xiaodong, LE MENACH Yvonnick, DUCREUX JeanPierre, PIRIOU Francis 
In this paper we compare three techniques to model the movement in 3D FEM using both classical formulations to solve the magnetic equations. To compare the methods a permanent magnet synchronous machine is modelled. The comparison is done at no load on the electromotive force and the cogging torque. 
[53] Determination of magnetic characteristics of a variable reluctance machine excited by DC and AC currents EPNC2004, 06/2004 TAÏBI Soufiane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[54] 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 
[55] Experimental determination of SMC material conductivity Proc. of EMF 2003, Aachen, Allemagne, 10/2003 BENABOU Abdelkader, CLENET Stéphane, PIRIOU Francis 
[56] Identification numérique des paramètres d’un MSLAP Numelec2003, 10/2003 TOUNZI Abdelmounaïm, ASKOUR Rachid, DUMETZ Eric, PIRIOU Francis 
[57] Adaptation of the Frequency Dependent JilesAtherton Model with B as entry variable ISEM 2003, Versailles, France, 05/2003 BENABOU Abdelkader, CLENET Stéphane, PIRIOU Francis 
[58] Comparison of the Preisach and JilesAtherton models to take hysteresis phenomenon into account in Finite Element Analysis EPNC 2002, Leuven, Belgium, 07/2002 BENABOU Abdelkader, CLENET Stéphane, PIRIOU Francis 
[59] Study of Head Winding Effects in a Switched Reluctance Machine Compumag2001, 07/2001 SOFIANE Yamina, TOUNZI Abdelmounaïm, PIRIOU Francis, LIESE Manfred 
[60] Error estimation for 3D magnetostatic problems coupled with electrical circuits procceding XVI EPNC, 09/2000 MARQUES Georges, LE MENACH Yvonnick, CLENET Stéphane, PIRIOU Francis 
[61] Modelling and Study of a Saturated PM Variable Reluctance Generator associated to a PWM Rectifier EPNC2000, pages. 7780, 09/2000 HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
[62] Design and study of a variable reluctance machine excited by a three phase current in the stator ICEM2000, Vol. 3, pages. 13941398, 08/2000 TAÏBI Soufiane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[63] Direct Torque Control of a wind driven induction generator connected to the grid through converters Electrimacs99, pages. 319324, 09/1999 BRULE Stéphane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[64] Comparison of induction machine Park’s models using parameters issue from FEM and from experimental tests ICEM98, Vol. 1, pages. 308313, 09/1998 BRULE Stéphane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[65] Study and vector control of a doubly slotted reluctance machine fed by a PWMVSI ICEM98, Vol. 3, pages. 21372142, 09/1998 HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
[66] Numerical modeling to study the vector control of an excited reluctance machine CEFC98, pages. 228, 06/1998 HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
[67] Design and optimisation of an excited reluctance generator using field computation COMPUMAG97, pages. 117118, 11/1997 HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
[68] Study of a variable reluctance generator for wind power conversion EPE97, Vol. 2, pages. 631636, 09/1997 HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
[69] Vector control of an autonomous induction generator connected to a PWM rectifier EPE97, Vol. 2, pages. 711716, 09/1997 COLLIEZ Claire, TOUNZI Abdelmounaïm, PIRIOU Francis 
[70] Study of an induction machine using Park’s model and Finite Element Method ICEM96, Vol. 2, pages. 2429, 09/1996 LEPLAT PierreMarie, TOUNZI Abdelmounaïm, CLENET Stéphane, PIRIOU Francis 
[71] Study of an autonomous induction generator connected to a PWM rectifier Electrimacs, Vol. 3, pages. 10891094, 09/1996 LEPLAT PierreMarie, TOUNZI Abdelmounaïm, CLENET Stéphane, PIRIOU Francis 
[72] Numerical modelling of an induction generator connected to a PWM voltage source inverter EPNC96, pages. 4348, 06/1996 LEPLAT PierreMarie, CLENET Stéphane, TOUNZI Abdelmounaïm, PIRIOU Francis 
ACN Conférence nationale avec acte 
[1] 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. 
[2] Modélisation d’une matrice issue de la méthode des éléments finis NUMELEC, 12/2008 TAILLARD Julien, GUYOMARC’H Frédéric, LE MENACH Yvonnick, PIRIOU Francis, DEKEYSER JeanLuc 
[3] 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 
[4] Etude en génératrice d’une Machine à Réluctance Variable à Double Saillance excitée EF 2005, 09/2005 TOUNZI Abdelmounaïm, PIRIOU Francis 
[5] Dimensionnement et caractérisation d’une machine à réluctance variable vernier excitée par un système triphasé au rotor EF2005, 09/2005 TOUNZI Abdelmounaïm, PIRIOU Francis 
[6] Etude en génératrice d’une Machine à Réluctance Variable à Double Saillance excitée EF2003, 11/2003 TOUNZI Abdelmounaïm, PIRIOU Francis 
[7] Etude de modèles d’hystérésis dynamiques en vue d’une implantation dans un code de calcul Eléments Finis Proc. of MGE 2003, Grenoble, France, 04/2003 BENABOU Abdelkader, CLENET Stéphane, PIRIOU Francis 
[8] Utilisation d’une procédure analytique associée à un modèle numérique pour la détermination des pertes fer d’une MRVDS (SRM) EF2001, pages. 379384, 11/2001 SOFIANE Yamina, TOUNZI Abdelmounaïm, PIRIOU Francis 
[9] Etude de la machine asynchrone avec un modèle diphasé tenant compte de la saturation et des effets croisés EF99, pages. 309314, 03/1999 BRULE Stéphane, TOUNZI Abdelmounaïm, PIRIOU Francis 
[10] Etude de MRV excitées pour des applications en entraînement direct CEMD99, pages. 8388, 02/1999 TAÏBI Soufiane, HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
[11] Production d’énergie décentralisée par un système Machine à Réluctance Variable  Convertisseurs statiques SEE, 03/1998 HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
[12] Etude d’une génératrice non conventionnelle pour une application en éolienne Congrès International en IEEA, pages. 7074, 12/1997 HAOUARA Ilhem, TOUNZI Abdelmounaïm, PIRIOU Francis 
AP Autre publication 
[1] Caractérisation et Modélisation de l’Hystérésis Scalaire Statique: Implantation dans un Code de Calcul Eléments Finis GDR Sûreté et Disponibilité des Systèmes Electrotechniques, 06/2001, Abstract AHMADA B., ALVES F., BEN ABDALLAH B., BENABOU Abdelkader, BERNARD Yves, BOUILLAULT Frédéric, CHABRERIE JeanPierre, CLENET Stéphane, FELIACHI Mouloud, LEBOUC Afef, MASSON JeanPierre, MENDES E, MEUNIER Gérard, NOURDINE Amir, OULED AMOR Yassine, PIRIOU Francis, SEGUI Yvan 
B. AHMADA, F. ALVES, B. BEN ABDALLAH, Abdelkader BENABOU, Y. BERNARD, F. BOUILLAULT, J.P. CHABRERIE, S. CLENET, M. FELIACHI, A. LEBOUC, J.P. MASSON, E. MENDES, G. MEUNIER, A. NOURDINE, Y. OULED AMOR, F. PIRIOU, Y. SEGUI. 
INV Conférence invité 
[1] 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 
OP Ouvrage pédagogique 
[1] Static formulations: Electrostatic, Electrokinetic, Magnetostatics The Finite Element Method for Electromagnetic Modeling,edited by G. Meunier, ISTE Wiley, pages. 69116, 01/2008 DULAR Patrick, PIRIOU Francis 
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