Un couplage FEM-BEM pour la modélisation de composites magnétoélectriques

International audience-Un couplage FEM-BEM basé sur une formulation en potentiel scalaire magnétique réduit est appliqué à la modélisation des composites magnétoélectriques. Une telle approche permet de ne pas considérer la région d'air et d'utiliser un unique maillage pour les sous-problèmes magnétiques, mécaniques et électriques qui oeuvre à l'effet magnétoélectrique. Un solveur Gauss-Seidel par bloc est mise en oeuvre pour résoudre le problème global. Mots clés-multiphysique, couplage FEM-BEM, composite magnétoélectrique

Application of Whitney elements for the reconstruction of electric arc current density in low-voltage circuit breakers

International audiencePurpose-This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a low-voltage circuit breaker. Design/methodology/approach-Considering that electric arc current density is a zero divergence vector field, the inverse problem can be solved in Whitney space W 2 in terms of electric current density J with the zero divergence condition as a constraint or can be solved in Whitney space W 1 in terms of electric vector potential T where the zero divergence condition naturally holds. Moreover, the tree gauging condition is applied to ensure a unique solution when solving for the vector potential in space W 1. Tikhonov regularization is used to treat the ill-posedness of the inverse problem complemented with L-curve method for the selection of regularization parameters. A common mode approach is proposed, which solves for the reduced electric vector potential representing the internal current loops instead of solving for the total electric vector potential. The proposed inversion approaches are numerically tested starting from simulated magnetic field values. Findings-With the common mode approach, the reconstruction of current density is significantly improved for both formulations using face elements in space W 2 and using edge elements in space W 1. When solving the inverse problem in space W 1 , the choice of the regularization operator has a key role to obtain a good reconstruction, where the discrete curl operator is a good option. The standard Tikhonov regularization obtains a good reconstruction with J-formulation, but fails in the case of T-formulation. The use of edge elements requires a tree-cotree gauging to ensure the uniqueness of T. Moreover, additional efforts have to be taken to find an optimal regularization operator and an optimal tree when using edge elements. In conclusion, the J-formulation is to be preferred

A FEM-BEM coupling for the modeling of linear magnetoelectric effects in composite structures

International audienceThe aim of this study is to model magnetoelectric effects involved in laminate composites made of magnetostrictive and piezoelectric materials. We therefore have to consider an electro-magneto-mechanical problem derived by coupling equations describing active materials, as Tefenol-D for magnetostrictive layers and PZT for piezoelectric layers [1]. The reference method for the resolution of this type of problems is the finite element method. Although this method is general and largely proven, it can be computationally expensive, especially for low-frequency electromagnetic problems where the resolution may require meshing the air and considering an infinite box to simulate the decay of electromagnetic fields at infinity. In our case, this method is well adapted to the modeling of electro-mechanical coupling. Indeed, the large permittivity of piezoelectric materials makes the electric field leaks negligible. It may become expensive for the modeling of the magneto-mechanical coupling especially if the volume of the active magnetic materials is very small compared to the volume of the air leading to a huge mesh with a lot of air. To solve this type of problem without having to mesh the air, coupling between finite element method for the active material and boundary element method for the air region have already been used with excellent results [2]. We will therefore use this type of method in the modeling of the magnetic problem. Although the magnetostrictive phenomenon is strongly nonlinear, we will consider it as linear as a first approximation. This approximation makes it dual to the piezoelectric phenomenon. The electro-magneto-mechanical coupling is therefore expressed by a linear matrix block system with sparse matrices for the mechanical and electrical problem and full matrices for the magnetic problem. The resulting linear system is solved using the Gauss-Seidel method with linear solvers adapted to the type of matrix, i.e, MUMPS used for sparse matrices and GMRES used for full matrices

COMPARISON BETWEEN EULERIAN AND LAGRANGIAN DESCRIPTION OF MOTION APPLICATION TO EDDY CURRENTS COMPUTATION IN CIRCUIT BREAKERS ELECTRODES

International audienceThis paper deals with the modeling of eddy currents generated by arc motion during opening phases of circuit breakers. The paper is mainly divided in two parts. The first part one consists in determining eddy currents in electrodes. Two descriptions of the motion are under test: The Eulerian one which is easy to implement but limited to invariant geometry and the Lagrangian one more general. Both descriptions are compared in order to validate Lagrangian one. Once validated, this method is used to calculate eddy current in splitter plates. All simulations are carried out with a T- FEM formulation and no new mesh at each time step is required

Design of a PCB Rogowski Coil : simulation and optimisation

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FFT-PEEC: A Fast Tool From CAD to Power Electronics Simulations

A fast and general Partial Element Equivalent Circuit (PEEC) method based on the Fast-Fourier-Transform (FFT) is proposed for the first time. The numerical tool only requires common CAD data input files (e.g. .stl format), then the discretization process is performed automatically by means of a fast voxelization technique based on ray intersection, thus drastically reducing the human effort required to setup the model. The method allows for considering at the same time inductive and capacitive effects, and is focused on power electronics applications where propagation effects can be neglected, whereas all the other electromagnetic phenomena are considered. Specifically, the proposed method is particularly suited for problems where both electric and magnetic fields are equally important and therefore quasistatic approximations do not apply. An ad-hoc preconditioner which significantly speeds-up the solver is also proposed and, thanks to the FFT, both memory and computation time are significantly reduced, without the need of applying data compression. Both linear and non-linear materials are considered by the proposed FFT-PEEC method. Sample implementation of the method is made publicly available