References of "Geuzaine, Christophe"
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See detailDouble sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem
Vion, Alexandre ULg; Geuzaine, Christophe ULg

in Journal of Computational Physics (2014), 266

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See detailEvaluation of shielding effectiveness of composite wall with a time domain discontinuous Galerkin method
Kameni, Abelin; Modave, Axel ULg; Boubekeur, Mohamed et al

in European Physical Journal : Applied physics (2013), 64(2), 24508

This article presents a Time Domain Discontinuous Galerkin method applied for solving the conservative form of Maxwell equations and computing the radiated fields in electromagnetic compatibility problems ... [more ▼]

This article presents a Time Domain Discontinuous Galerkin method applied for solving the conservative form of Maxwell equations and computing the radiated fields in electromagnetic compatibility problems. The results obtained in homogenous media for the transverse magnetic waves are validated in two cases. We compare our solution to an analytical solution of Maxwell’s equations based on characteristic method. Our results on shielding effectiveness of a conducting wall are same as those obtained from analytical expression in frequency domain. The propagation in heterogeneous medium is explored. The shielding effectiveness of a composite wall partially filled by circular conductives inclusions is computed. The proposed results are in conformity with the classical predictive homogenizations rules. [less ▲]

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See detailAn optimum PML for scattering problems in the time domain
Modave, Axel ULg; Kameni, Abelin; Lambrechts, Jonathan et al

in European Physical Journal : Applied physics (2013), 64(2), 24502

In electromagnetic compatibility, scattering problems are defined in an infinite spatial domain, while numerical techniques such as finite element methods require a computational domain that is bounded ... [more ▼]

In electromagnetic compatibility, scattering problems are defined in an infinite spatial domain, while numerical techniques such as finite element methods require a computational domain that is bounded. The perfectly matched layer (PML) is widely used to simulate the truncation of the computational domain. However, its performance depends critically on an absorption function. This function is generally tuned by using case-dependent optimization procedures. In this paper, we will present some efficient functions that overcome any tuning. They will be compared using a realistic scattering benchmark solved with the Discontinuous Galerkin method. [less ▲]

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See detailDouble sweep preconditioner for Schwarz methods applied to the Helmholtz equation
Vion, Alexandre ULg; Geuzaine, Christophe ULg

in Proceedings of the 22nd International Conference on Domain Decomposition Methods (2013, September)

Observing that the optimized Schwarz algorithm is equivalent to the solution of a linear system, we design a new preconditioner as an approximate inverse of the iteration operator, in the particular case ... [more ▼]

Observing that the optimized Schwarz algorithm is equivalent to the solution of a linear system, we design a new preconditioner as an approximate inverse of the iteration operator, in the particular case of a layered decomposi- tion. We show that it can be rewritten as two independent sequences of subproblem solves (forward and back- ward), hence the name ‘double sweep’. The whole algorithm is implemented as a matrix-free GMRES iteration, that requires no more additional preprocessing than the original algorithm. Numerical experiments indicate that the convergence rate is independent of the wavenumber and number of subdomains when good approximations of the DtN maps are used, in both homogeneous and non-homogeneous cases. [less ▲]

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See detailModelling Time Reversal Applications in a Reverberation Chamber using the Current Image Method
Spirlet, Maxime; Broun, Valery; Camus, Philippe et al

Conference (2013, September)

In this paper, we present a numerical model to analyze Time Reversal applications in a reverberation chamber using the current image method. The principles behind this numerical model are presented in the ... [more ▼]

In this paper, we present a numerical model to analyze Time Reversal applications in a reverberation chamber using the current image method. The principles behind this numerical model are presented in the first part of the paper. The major advantage of this reverberation chamber model is that it requires a lot less computing time than usual solvers with qualitatively satisfying results. Next, an extension of our method to model Time Reversal Mirrors in reverberating cavities is described. Finally, two examples of Time Reversal refocusing using Time Reversal Mirrors of one or several elements are presented for illustration. [less ▲]

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See detailSubproblem Approach for Modeling Multiply Connected Thin Regions with an h-Conformal Magnetodynamic Finite Element Formulation
Dang, Quoc Vuong ULg; Dular, Patrick ULg; Vazquez Sabariego, Ruth ULg et al

in European Physical Journal : Applied physics (2013), in press

A subproblem h-conformal eddy current nite element method is proposed for correcting the inaccuracies inherent to thin shell models. Such models replace volume thin regions by surfaces but neglect border ... [more ▼]

A subproblem h-conformal eddy current nite element method is proposed for correcting the inaccuracies inherent to thin shell models. Such models replace volume thin regions by surfaces but neglect border e ects in the vicinity of their edges and corners. The developed surface-to-volume correction problem is de ned as a step of the multiple subproblems that can split a complete problem, consisting of inductors and magnetic or conducting regions, some of these being thin regions. The general case of multiply connected thin regions is considered [less ▲]

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See detailA multirate approach to combine electromagnetic transients and fundamental-frequency simulations
Plumier, Frédéric ULg; Geuzaine, Christophe ULg; Van Cutsem, Thierry ULg

in Proc. 10th International Conference on Power System Transients (2013, July)

Abstract--- A new multi-rate technique is proposed to combine fundamental-frequency simulation (typical of stability studies) with electromagnetic transients simulation. The objective of this hybrid ... [more ▼]

Abstract--- A new multi-rate technique is proposed to combine fundamental-frequency simulation (typical of stability studies) with electromagnetic transients simulation. The objective of this hybrid approach is to obtain more accurate simulations than with the fundamental-frequency approximation, while saving computing time by applying the detailed model to a subsystem only, in some neighbourhood of the disturbance. It also allows to remove some limitations of fundamental-frequency simulation, such as the difficulty of simulating unbalanced faults. A relaxation technique is used to iterate between both models with simple interfacing. Preliminary results obtained with a 74-bus test system are presented, together with a comparison with full electromagnetic transients simulation. [less ▲]

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See detailNonlinear Computational Homogenization Method for the Evaluation of Eddy Currents in Soft Magnetic Composites
Niyonzima, Innocent ULg; Sabariego, Ruth Vazquez; Dular, Patrick ULg et al

in Proceedings of the 19th Conference on the Computation of Electromagnetic Fields (COMPUMAG2013) (2013, July)

In this paper, a heterogeneous multiscale method (HMM) technique is applied to model the behaviour of electromagnetic fields in soft magnetic composites (SMC). Two problems are derived from the two-scale ... [more ▼]

In this paper, a heterogeneous multiscale method (HMM) technique is applied to model the behaviour of electromagnetic fields in soft magnetic composites (SMC). Two problems are derived from the two-scale homogenization theory: a macroscale problem that captures the slow variations of the overall solution, and many mesoscale problems that allow determining the constitutive laws at the macroscale. As application, an SMC core is considered. [less ▲]

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See detailFifth International Conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011)
Béchet, Eric ULg; Dick, Erik; Geuzaine, Christophe ULg et al

in International Journal of Computational & Applied Mathematics (2013), 246

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See detailAn Energy-Based Variational Model of Ferromagnetic Hysteresis for Finite Element Computations
François-Lavet, Vincent ULg; Henrotte, François; Stainier, Laurent ULg et al

in Journal of Computational & Applied Mathematics (2013), 246

This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic ... [more ▼]

This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hysteresis loops as is usually the case. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. [less ▲]

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See detailA PML for convex truncated domains in time-dependent acoustics with a DG-FE discretization
Modave, Axel ULg; Lambrechts, Jonathan; Delhez, Eric ULg et al

in Proceedings of the 11th International Conference on Mathematical and Numerical Aspects of Waves (WAVES 2013) (2013, June 03)

A new perfectly matched layer (PML) is proposed for convex truncated domains in the context of time-dependent acoustics. With this formulation, the size of the computational domain can be reduced when ... [more ▼]

A new perfectly matched layer (PML) is proposed for convex truncated domains in the context of time-dependent acoustics. With this formulation, the size of the computational domain can be reduced when classical shapes of truncated domains are less appropriate. A numerical discretization based on the discontinuous Galerkin method is then described and validated. An example of realistic three-dimensional application is finally proposed. [less ▲]

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See detailComputational Homogenization for Laminated Ferromagnetic Cores in Magnetodynamics
Niyonzima, Innocent ULg; V Sabariego, Ruth; Dular, Patrick ULg et al

in IEEE Transactions on Magnetics (2013), 49(5), 2049-2052

In this paper, we investigate the modeling of ferromagnetic multiscale materials. We propose a computational homogenization technique based on the heterogeneous multiscale method (HMM) that includes both ... [more ▼]

In this paper, we investigate the modeling of ferromagnetic multiscale materials. We propose a computational homogenization technique based on the heterogeneous multiscale method (HMM) that includes both eddy-current and hysteretic losses at the mesoscale. The HMM comprises: 1) a macroscale problem that captures the slow variations of the overall solution; 2) many mesoscale problems that allow to determine the constitutive law at the macroscale. As application example, a laminated iron core is considered. [less ▲]

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See detailComputing Bounds on the Geometrical Quality of 2D Curvilinear Finite Elements
Johnen, Amaury ULg; Remacle, J.-F.; Toulorge, T. et al

Conference (2013, April 25)

The development of high-order computational methods for solving partial differen- tial equations on unstructured grids has been underway for many years. Such meth- ods critically depend on the ... [more ▼]

The development of high-order computational methods for solving partial differen- tial equations on unstructured grids has been underway for many years. Such meth- ods critically depend on the availability of high-quality curvilinear meshes, as one badly-shaped element can degrade the solution in the whole domain (J. Shewchuk, “What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures”, Preprint, 2002). The usual way of generating curved meshes is to first generate a straight sided mesh and to curve mesh entities that are classified on the boundaries of the domain. The latter operation introduces a “shape-distortion” that should be controlled if we suppose that the straight sided mesh is composed of well-shaped elements. Quality measures allow to quantify to which point an element is well-shaped. They also provide tools to improve the quality of meshes through optimization opera- tions. Many quality measures has been proposed for quadratic triangular finite element. Recently, X. Roca et al. (“Defining Quality Measures for High-Order Planar Triangles and Curved Mesh Generation”, Proceedings of the 20th Interna- tional Meshing Roundtable, 2011) proposed a technique that allows extending any Jacobian based quality measure for linear elements to high-order iso-parametric planar triangles of any interpolation degree. In this work we propose an efficient method to provide accurate bounds on the mag- nitude of the shape distortion of any triangular and quadrangular curved element. The shape distortion is measured with respect to an ideal element, which can e.g. be an equilateral triangle or the element from the original straight-sided mesh. The key feature of the method is that we can adaptively expand functions based on the Jacobian matrix and its determinant in terms of Be ́zier functions. Be ́zier functions have both properties of boundedness and positivity, which allow sharp computation of minimum or maximum of the interpolated functions. [less ▲]

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See detailEvaluation of Shielding Effectiveness in the Time Domain using a DG Method with an Efficient PML
Modave, Axel ULg; Geuzaine, Christophe ULg; Boubekeur, Mohamed et al

Poster (2013, April 24)

Development of new electric and electronic devices leads to an increasing importance for solving electromagnetic compatibility problems. In particular, the optimization of radiated emissions is ... [more ▼]

Development of new electric and electronic devices leads to an increasing importance for solving electromagnetic compatibility problems. In particular, the optimization of radiated emissions is increasingly done through numerical modeling. In this context, numerical methods allow to evaluate the effectiveness of more and more elaborate shielding enclosures. We propose an application of the nodal Discontinuous Galerkin method to evaluate the effectiveness of composite shieldings in the time domain. This numerical method provides convenient advantages to deal with shielding problems. Firstly, heterogeneous media are naturally included in the discrete formulation. After, the method is famous to allow a massive parallelization for the numerical resolution. Finally, a resolution in the time domain allows to consider transient signals. The numerical scheme is firstly validated using an academic benchmark. In the same way, the PML used to truncate the computational domain is optimized and validated. Applications are then presented for homogeneous and composite shieldings. The preliminary results are in conformity with classical predictive rules. [less ▲]

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See detailSubproblem h-Conform Formulation for Accurate Thin Shell Models Between Conducting and Nonconducting Regions
Dang, Quoc Vuong ULg; Dular, Patrick ULg; Vazquez Sabariego, Ruth ULg et al

in Proceeding of the 9th International Symposium on Electric and Magnetic Fields, EMF 2013 (2013, April 23)

A subproblem method (SPM) with h-formulation is developed for correcting the inaccuracies near edges and corners that arise from using thin shell (TS) models to replace thin volume regions by surfaces ... [more ▼]

A subproblem method (SPM) with h-formulation is developed for correcting the inaccuracies near edges and corners that arise from using thin shell (TS) models to replace thin volume regions by surfaces. The developed surface-to-volume correction problem is defined as a step of multiple SPs, with inductors and magnetic or conducting regions, some of them being thin. The TS model assumes that the fields in the thin regions are approximated by a priori 1-D analytical distributions along the shell thickness (C. Geuzaine et al., “Dual formulations for the modeling of thin electromagnetic shells using edge elements,” IEEE Trans. Magn., vol. 36, no. 4, pp. 799–802, 2000). Their interior is not meshed and ratherextracted from the studied domain, which is reduced to a zero-thickness double layer with interface conditions (ICs) linked to 1-D analytical distributions that however neglect end and curvature effects. This leads to inaccuracies near edges and corners that increase with the thickness. To cope with these difficulties, the authors have recently proposed a SPM based on the h-formulation for a thin region located between non-conducting regions (Vuong Q. Dang et al., “Subproblem Approach for Thin Shell Dual Finite Element Formulations”, IEEE Trans. Magn., vol. 48, no. 2, pp. 407–410, 2012). The magnetic field h is herein defined in nonconducting regions by means of a magnetic scalar potential , i.e. h = -grad{\phi} , with discontinuities of through the TS. In this paper, the SPM is extended to account for thin regions located between conducting regions or between conducting and nonconducting regions, in the general case of multiply connected regions. In these regions, the potential is not defined anymore on both sides of the TS and the problem has to be expressed in terms of the discontinuities of h, possibly involving on one side only, to be strongly defined via an IC through the TS. In the proposed SP strategy, a reduced problem with only inductors is first solved on a simplified mesh without thin and volume regions. Its solution gives surface sources (SSs) as ICs for added TS regions, and volume sources (VSs) for possible added volume regions. The TS solution is further improved by a volume correction via SSs and VSs that overcome the TS assumptions, respectively suppressing the TS model and adding the volume model. Each SP has its own separate mesh, which increases the computational efficiency. Details on the proposed method will be given in the extended paper, with practical applications. [less ▲]

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See detailA Computational Homogenization Method for the Evaluation of Eddy Current in Nonlinear Soft Magnetic Composites
Niyonzima, Innocent ULg; Vazquez Sabariego, Ruth ULg; Dular, Patrick ULg et al

in Proceeding of the 9th International Symposium on Electric and Magnetic Fields, EMF 2013 (2013, April 23)

The use of the soft magnetic composite (SMC) in electric devices has increased in recent years. These materials made from a metallic powder compacted with a dielectric binder are a good alternative to ... [more ▼]

The use of the soft magnetic composite (SMC) in electric devices has increased in recent years. These materials made from a metallic powder compacted with a dielectric binder are a good alternative to laminated ferromagnetic structures as their granular mesoscale structure allows to significantly reduce the eddy current losses. Furthermore unlike the laminated ferromagnetic structures, SMC exhibit isotropic magnetic properties what makes them good candidates for manufacturing machines with 3D flux paths. The isotropy of the thermal conductivity also allows for a more efficient heat dissipation. The use of classical numerical methods such as the finite element method to study the behavior of SMC is computational very expensive. Indeed a very fine mesh would be required in order to capture fine scale variations i.e. variations at level of metallic grains whence the use of multiscale methods for modelling SMC. The application of multiscale method to study the behaviour of SMC is relatively recent. In (A. Bordianu et al “A Multiscale Approach to Predict Classical Losses in Soft Magnetic Composites”, IEEE Trans. Mag., vol. 48, no. 4, 2012.), the authors used a homogenization technique to compute electrical and magnetic constitutive laws on a representative volume element (RVE). These laws were then used in finite element computations. Herein, the RVE has been chosen to account for the grain- grain contact that can occur in a actual SMC structure due to the compaction process and that can lead to the appearance of macroscale eddy currents. In this paper, we will extend the computational homogenization method success- fully used for modelling the behaviour of laminated ferromagnetic cores in mag- netodynamics (I. Niyonzima et al “Computational Homogenization for Laminated Ferromagnetic Cores in Magnetodynamics”, in Proc. of the 15th Biennal Confer- ence on Electromagnetic Field Computation, 2012) to the case of SMC. The method is based on the heterogeneous multiscale method (HMM) and couples two types of problems: a macroscale problem that captures the slow variations of the overall so- lution and many microscale problems that allow to determine the constitutive laws at the macroscale. The choice of RVE will also be discussed. [less ▲]

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See detailDual Formulations for Accurate Thin Shell Models in a Finite Element Subproblem Method
Dang, Quoc Vuong ULg; Dular, Patrick ULg; Vazquez Sabariego, Ruth ULg et al

in Proceeding of the 19th COMPUMAG Conference on the Computation of Electromagnetic Fields, 2013 (2013, April 01)

A subproblem finite with dual finite element magnetostatic and magnetodynamic formulations is developed for correcting the inaccuracies near edges and corners coming from thin shell models, that replace ... [more ▼]

A subproblem finite with dual finite element magnetostatic and magnetodynamic formulations is developed for correcting the inaccuracies near edges and corners coming from thin shell models, that replace thin volume regions by surfaces. The surface-to-volume correction problem is defined as one of the multiple subproblems applied to a complete problem, considering successive additions of inductors and magnetic or conducting regions, some of these being thin regions. Each SP requires a proper adapted mesh of its regions, which facilitates meshing and increases computational e ciency. [less ▲]

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See detailOptimized Schwarz Algorithm with Double Sweep Preconditioner for the Helmholtz Equation
Vion, Alexandre ULg; Geuzaine, Christophe ULg

in Proceedings of the 9th International Symposium on Electric and Magnetic Fields, EMF 2013 (2013, April)

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