Transformation Optics, Generalized Cloaking and Superlenses

In this paper, transformation optics is presented together with a generalization of invisibility cloaking: instead of an empty region of space, an inhomogeneous structure is transformed via Pendry's map in order to give, to any object hidden in the central hole of the cloak, a completely arbitrary appearance. Other illusion devices based on superlenses considered from the point of view of transformation optics are also discussed.Comment: 7 pages (two columns), 9 figures, to appear in IEEE Trans. Mag., invited paper in Compumag 2009 (Florianopolis, Brasil), corresponding slides available on http://www.fresnel.fr/perso/nicolet

Waveform Relaxation for the Computational Homogenization of Multiscale Magnetoquasistatic Problems

This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the Newton--Raphson scheme. The resolution of many mesoscale problems per Gauss point allows to compute the homogenized constitutive law and its derivative by finite differences. In the proposed approach, the macroscale problem and the mesoscale problems are weakly coupled and solved separately using the finite element method on time intervals for several waveform relaxation iterations. The exchange of information between both problems is still carried out using the heterogeneous multiscale method. However, the partial derivatives can now be evaluated exactly by solving only one mesoscale problem per Gauss point.Comment: submitted to JC

On the O(1) Solution of Multiple-Scattering Problems

In this paper, we present a multiple-scattering solver for nonconvex geometries such as those obtained as the union of a finite number of convex surfaces. For a prescribed error tolerance, this algorithm exhibits a fixed computational cost for arbitrarily high frequencies. At the core of the method is an extension of the method of stationary phase, together with the use of an ansatz for the unknown density in a combined-field boundary integral formulation

Harcèlement moral au travail. Etat des lieux et pistes de développement.

Revue théorique critique et analyse de littérature sur le harcèlement moralPeer reviewe

Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems Using Magnetic Induction Conforming Formulations

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and many mesoscale problems defined on finely-meshed small areas around some points of interest of the macroscale mesh (e.g. numerical quadrature points). The exchange of information between these macro and meso problems is thoroughly explained in this paper. For the sake of validation, we consider a two-dimensional geometry of an idealized periodic soft magnetic composite.Comment: Paper accepted for publication in the SIAM MMS journa

Three beneficiaries of project-oriented education in power electronics

peer reviewedPower Electronics education at the University of Liège exhibits a particular feature, in that a person from industry is directly involved in the teaching of the introductory Power Electronics course since academic year 2007-2008. Together with him, we teach this subject making use of a project-oriented method. After two years of this experience, it is now of great interest to analyze the main benefits of this method for the students, the teaching team at the University and the company involved in the teaching process. In this paper we present through an example the method that is being used. We mention some interesting technical problems encountered by the students during their project work. We also present the evolution of the method from the first year of application in 2007-2008 to the forthcoming third year in 2009-2010.OptiSHE

Numerical simulation of the magnetization of high-temperature superconductors: 3D finite element method using a single time-step iteration

We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects associated with currents that are not perpendicular to the local magnetic induction. We consider samples that are subjected to a uniform magnetic field varying linearly with time. Their magnetization is calculated by means of a weak formulation in the magnetostatic approximation of the Maxwell equations (A-phi formulation). An implicit method is used for the temporal resolution (Backward Euler scheme) and is solved in the open source solver GetDP. Picard iterations are used to deal with the power law conductivity of HTS. The finite element formulation is validated for an HTS tube with large pinning strength through the comparison with results obtained with other well-established methods. We show that carrying the calculations with a single time-step (as opposed to many small time-steps) produce results with excellent accuracy in a drastically reduced simulation time. The numerical method is extended to the study of the trapped magnetization of cylinders that are drilled with different arrays of columnar holes arranged parallel to the cylinder axis

Numerical investigation of a 3D hybrid high-order method for the indefinite time-harmonic Maxwell problem

Hybrid High-Order (HHO) methods are a recently developed class of methods belonging to the broader family of Discontinuous Sketetal methods. Other well known members of the same family are the well-established Hybridizable Discontinuous Galerkin (HDG) method, the nonconforming Virtual Element Method (ncVEM) and the Weak Galerkin (WG) method. HHO provides various valuable assets such as simple construction, support for fully-polyhedral meshes and arbitrary polynomial order, great computational efficiency, physical accuracy and straightforward support for hp-refinement. In this work we propose an HHO method for the indefinite time-harmonic Maxwell problem and we evaluate its numerical performance. In addition, we present the validation of the method in two different settings: a resonant cavity with Dirichlet conditions and a parallel plate waveguide problem with a total/scattered field decomposition and a plane-wave boundary condition. Finally, as a realistic application, we demonstrate HHO used on the study of the return loss in a waveguide mode converter

Perfectly Matched Layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates

In this paper, we first propose a general strategy to implement the Perfectly Matched Layer (PML) approach in the most standard numerical schemes used for simulating the dynamics of nonlinear Schrödinger equations. The methods are based on the time-splitting [15] or relaxation [24] schemes in time, and finite element or FFT-based pseudospectral discretization methods in space. A thorough numerical study is developed for linear and nonlinear problems to understand how the PML approach behaves (absorbing function and tuning parameters) for a given scheme. The extension to the rotating Gross-Pitaevskii equation is then proposed by using the rotating Lagrangian coordinates transformation method [13, 16, 39], some numerical simulations illustrating the strength of the proposed approach