Geometrical Validity of High-Order Triangular Finite Elements

in Engineering with Computers (in press)

This paper presents a method to compute accurate bounds on Jacobian determinants of high-order (curvilinear) triangular nite elements. This method can be used to guarantee that a curvilinear triangle is ... [more ▼]

This paper presents a method to compute accurate bounds on Jacobian determinants of high-order (curvilinear) triangular nite elements. This method can be used to guarantee that a curvilinear triangle is geometrically valid, i.e., that its Jacobian determinant is strictly positive everywhere in its reference domain. It also provides an e cient way to measure the quality the triangles. The key feature of the method is to expand the Jacobian determinant using a polynomial basis, built using B ezier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. [less ▲]

An Energy-Based Variational Model of Ferromagnetic Hysteresis for Finite Element Computations

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 ▲]

Computational Homogenization for Laminated Ferromagnetic Cores in Magnetodynamics

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 ▲]

Subproblem h-Conform Formulation for Accurate Thin Shell Models Between Conducting and Nonconducting Regions

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 ▲]

Homogenisation of Windings and Laminations in Time-Domain Finite-Element Modeling of Electrical Machines

in Proceedings of the 15th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC2012) (2012, November)

This paper deals with time-domain homogenisation of multi-turn windings and laminated cores in 2D and 3D finite- element (FE) modelling of rotating electrical machines. Herein the number of additional ... [more ▼]

This paper deals with time-domain homogenisation of multi-turn windings and laminated cores in 2D and 3D finite- element (FE) modelling of rotating electrical machines. Herein the number of additional degrees of freedom (auxiliary field variables) in the homogenised regions can be fixed depending on the extent of the eddy current effects and on the desired accuracy. The homogenisation technique is illustrated and validated by means of a 2D model of a switched reluctance motor. Global quantities, such as the phase impedance, converge very well to those produced by a precise but very expensive 3D model. [less ▲]

Time-domain finite-element modelling of laminated iron cores – Large skin effect homogenization considering the Jiles-Atherton hysteresis model

in Proceedings of the 15th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC2012) (2012, November)

This paper deals with the incorporation of the Jiles- Atherton (J-A) hysteresis model in a time-domain finite-element homogenization technique for laminated iron cores. The separate discretization of each ... [more ▼]

This paper deals with the incorporation of the Jiles- Atherton (J-A) hysteresis model in a time-domain finite-element homogenization technique for laminated iron cores. The separate discretization of each lamination is avoided by using dedicated skin-effect basis functions, which also serve to interpolate the J- A hysteretic material law. As validation test case, a stacked ring core surrounded by a toroidal coil is considered. [less ▲]

Multiscale Quasistatic Homogenization for Laminated Ferromagnetic Cores

in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC 2012) (2012, July 03)

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

In this paper, we investigate the modeling of ferromagnetic multiscale materials. We propose a computational homogenization method based on the heterogeneous multiscale method (HMM) with inclusion of a hysteresis model. The HMM involves: 1) a macroscale problem that captures the slow variations of the overall solution; 2) many microscale problems that allow to determine the constitutive law at the macroscale. At the microscale, a novel energy consistent hystere- sis model is incorporated. As application example, a laminated iron core is considered. [less ▲]

Evaluation de l'efficacité de blindage de parois hétérogènes par une méthode de Galerkin discontinue en domaine temporel

in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC2012) (2012, July)

ONELAB: Open Numerical Engineering LABoratory

in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC2012) (2012, July)

Combining Full Transients and Phasor Approximation Models in Power System Time Simulation

in Proceedings of the 21th International Conference on Domain Decomposition Methods (DD21) (2012, June)