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1. Corner asymptotics of the magnetic potential in the eddy-current model

Author

Dauge, Monique, Dular, Patrick, Krähenbühl, Laurent, Péron, Victor, Perrussel, Ronan, and Poignard, Clair

Subjects
Mathematics - Numerical Analysis
Abstract

In this paper, we describe the magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the corner asymptotic expansion for this potential as the distance to the corner goes to zero. This expansion involves singular functions and singular coefficients. We introduce a method for the calculation of the singular functions near the corner and we provide two methods to compute the singular coefficients: the method of moments and the method of quasi-dual singular functions. Estimates for the convergence of both approximate methods are proven. We eventually illustrate the theoretical results with finite element computations. The specific non-standard feature of this problem lies in the structure of its singular functions: They have the form of series whose first terms are harmonic polynomials and further terms are genuine non-smooth functions generated by the piecewise constant zeroth order term of the operator.

Published
2022
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3. Gradient-prolongation commutativity and graph theory

Author

Musy, François, Nicolas, Laurent, and Perrussel, Ronan

Subjects
Mathematics - Numerical Analysis
Abstract

This Note gives conditions that must be imposed to algebraic multilevel discretizations involving at the same time nodal and edge elements so that a gradient-prolongation commutativity condition will be satisfied; this condition is very important, since it characterizes the gradients of coarse nodal functions in the coarse edge function space. They will be expressed using graph theory and they provide techniques to compute approximation bases at each level., Comment: 6 pages

Published
2007
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4. Solution of the time-harmonic Maxwell equations using discontinuous Galerkin methods

Author

Dolean, Victorita, Fol, Hugo, Lanteri, Stephane, and Perrussel, Ronan

Subjects
Mathematics - Numerical Analysis
Abstract

We present numerical results concerning the solution of the time-harmonic Maxwell's equations discretized by discontinuous Galerkin methods. In particular, a numerical study of the convergence, which compares different strategies proposed in the literature for the elliptic Maxwell equations, is performed in the two-dimensional case., Comment: Preprint submitted for publication for the proceedings of ICCAM06 (11/04/2007)

Published
2006

5. Domain Decomposition for 3-D Nonlinear Magnetostatic Problems: Newton–Krylov–Schur Versus Schur–Newton–Krylov Methods

Author

Ghenai, Mohamed I., Perrussel, Ronan, Chadebec, Olivier, Vi, Frederic, Guichon, Jean-Michel, Meunier, Gerard, and Siau, Jonathan

Abstract

Domain decomposition is a strategy designed to be used on parallel machines. This strategy leads to hybrid methods between direct and iterative solvers and allows users to benefit from the advantages of both. Lately, the growing size of simulations in electromagnetics brought to light the interest of using domain decomposition. Nonlinearity is also one of the problem specificities where the need for an efficient solver is high. This article provides a comparison between two techniques of domain decomposition for solving 3-D nonlinear magnetostatic problems. A contactor test case with two nonlinear materials was used to estimate the performances of both methods.

Published
2024
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9. Algebraic Multigrid Methods for discrete Stokes and Oseen problems

Author

Napov, Artem, Notay, Yvan, Delandtsheer, Anne, Dohet-Eraly, Jérémy, Vuik, Cornelis, Perrussel, Ronan, Bacq, Pierre-Loic, Napov, Artem, Notay, Yvan, Delandtsheer, Anne, Dohet-Eraly, Jérémy, Vuik, Cornelis, Perrussel, Ronan, and Bacq, Pierre-Loic

Abstract

We investigate the numerical solution of saddle-point linear systems arising from the discretizationof Stokes and Oseen problems. We consider all-at-once algebraic multigrid (AMG) methods whichtypically struggle when applied to such systems. To avoid the usual difficulties, we introduce anew approach called the transform-then-solve approach. The key idea is to first apply an algebraictransformation to the linear system in order to give it a more suitable structure for the subsequentapplication of a relatively standard aggregation-based AMG method.The investigation of typical (low-order) finite elements discretization of Stokes problems show thatthe method is robust on a broad range of problems, even for variable viscosity or time-dependentproblems used in an industrial framework. The main challenge consists in improving the compet-itiveness of the method with respect to reference methods, because of the higher computationalcost of the method due to the algebraic transformation. To mitigate it, we implement two strate-gies which efficiently reduce the computational cost. As a consequence, the transform-then-solveapproach is competitive and significantly more robust.The method developed during the thesis is sequential by design. However, the use of parallelarchitecture has been shown to speed up significantly computations. As such, we also look at thealgorithmic changes needed to develop a parallel version of the transform-then-solve approach.We show that these changes do not impact the robustness of the method.The development of an AMG method for Oseen problems is more complicated because of thenon-symmetry of the velocity block. By using the convergence theory we develop in the thesis,we are able to show that it is possible to design a two-grid method which presents a convergenceindependent of the mesh size and the Reynolds number for constant convection problem. The keycondition is that the aggregation of the pressure unknowns follows the same pattern as the one of, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

Published
2022

11. Approximate conditions replacing thin layers

Author

Poignard, Clair, Dular, Patrick, Perrussel, Ronan, Krahenbuhl, Laurent, Nicolas, Laurent, and Schatzman, Michelle

Subjects
Electromagnetic fields -- Models, Electromagnetic fields -- Analysis, Finite element method -- Usage, Business, Electronics, Electronics and electrical industries
Abstract

We provide a rigorous asymptotic method to build approximate conditions equivalent to a thin layer. With these conditions the electromagnetic field may be computed in domains such as a biological cell, without meshing the membrane. The influence of the membrane is replaced by an appropriate condition on the inner domain, while in the thin layer, the approximate field is explicitly known. We give error estimates, which validate our asymptotic method, and we present a few numerical results performed with the finite-element method. Index Terms--Asymptotic methods, finite-element method, thin layers.

Published
2008

12. Optimized Schwarz algorithms for solving time-harmonic Maxwell's equations discretized by a discontinuous Galerkin method

Author

Dolean, Victorita, Lanteri, Stephane, and Perrussel, Ronan

Subjects
Bayesian information criterion -- Analysis, Maxwell equations -- Analysis, Three-dimensional display systems -- Usage, 3D technology, Business, Electronics, Electronics and electrical industries
Abstract

The numerical solution of the three-dimensional time-harmonic Maxwell equations using high order methods such as discontinuous Galerkin formulations require efficient solvers. A domain decomposition strategy is introduced for this purpose. This strategy is based on optimized Schwarz methods applied to the first order form of the Maxwell system and leads to the best possible convergence of these algorithms. The principles are explained for a 2D model problem and numerical simulations confirm the predicted theoretical behavior. The efficiency is further demonstrated on more realistic 3D geometries including a bioelectromagnetism application. Index Terms--Discontinuous Galerkin methods, domain decomposition methods, optimized interface conditions.

Published
2008

13. Post processing for the vector finite element method: accurate computing of dual field

Author

Vollaire, Christian, Musy, Francois, and Perrussel, Ronan

Subjects
Finite element method -- Usage, Harmonic functions -- Analysis, Vector graphics -- Electric properties, Vector graphics -- Magnetic properties, Business, Electronics, Electronics and electrical industries
Abstract

An accurate method to compute dual field in high frequency time harmonic problem is presented. From a primal field obtained by a vector finite element discretization, the dual field is obtained without numerical derivation by using a least square argument. The accuracy of the method is compared with the natural method using shape function derivatives. Index Terms--Edge elements, finite element method, post-processing.

Published
2006

14. An efficient preconditioner for linear systems issued from the finite-element method for scattering problems

Author

Perrussel, Ronan, Nicolas, Laurent, and Musy, Francois

Subjects
Electromagnetism -- Research, Business, Electronics, Electronics and electrical industries
Abstract

An efficient preconditioner for systems issued from the finite element discretization of time harmonic Maxwell's equations with absorbing boundary conditions is presented. It is based on the Helmholtz decomposition of the electromagnetic field and its discrete counterpart. It is compared to a classical preconditioner on both simple and realistic problems. Its behavior is also evaluated on meshes showing different characteristics. Index Terms--Electromagnetic fields, finite-element methods, numerical analysis, scattering.

Published
2004

16. Algebraic analysis of two-level multigrid methods for edge elements. ETNA - Electronic Transactions on Numerical Analysis

Author

Napov, Artem and Perrussel, Ronan

Subjects
convergence analysis, multigrid, algebraic multigrid, two-level multigrid, Reitzinger-Schöberl multigrid, preconditioning, aggregation, edge elements,Mathematics, Physics and Space Research
Abstract

We present an algebraic analysis of two-level multigrid methods for the solution of linear systems arising from the discretization of the curl-curl boundary value problem with edge elements. The analysis is restricted to the singular compatible linear systems as obtained by setting to zero the contribution of the lowest order (mass) term in the associated partial differential equation. We use the analysis to show that for some discrete curl-curl problems, the convergence rate of some Reitzinger-Schöberl two-level multigrid variants is bounded independently of the mesh size and the problem peculiarities. This covers some discretizations on Cartesian grids, including problems with isotropic coefficients, anisotropic coefficients and/or stretched grids, and jumps in the coefficients, but also the discretizations on uniform unstructured simplex grids.

Published
2019

17. Homogenization of lamination stacks based on the vector potential formulation

Author

Issa, Mohammad, Krähenbühl, Laurent, Poignard, Clair, Poirier, Jean-René, Perrussel, Ronan, LAboratoire PLasma et Conversion d'Energie (LAPLACE), Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Équipe Calcul scientifique et Modélisation, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Groupe de Recherches en Electrodynamique (LAPLACE-GREM3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), and Groupe de Recherche en Electromagnétisme (LAPLACE-GRE)

Subjects
asymptotic expansion, [SPI.NRJ]Engineering Sciences [physics]/Electric power, Classical homogenization
Abstract

International audience; We present an effective modelling of a lamination stack in 1d using classical homogenization and a correction for the interface between the air and the lamination stack. We consider the case where the skin depth is kept less than or equal to the thickness of one metal sheet.

Published
2019

18. Revisiting aggregation-based multigrid for edge finite elements

Author

Napov, Artem and Perrussel, Ronan

Subjects
Aggregation, Edge elements, Algebraic multigrid, Preconditioning, Analyse numérique
Abstract

We consider a modification of the Reitzinger-Schöberl algebraic multigrid method for the iterative solution of the curl-curl boundary value problem discretized with edge elements. The Reitzinger-Schöberl method is attractive for its low memory requirements and moderate cost per iteration, but the number of iterations typically tends to increase with the problem size. Here we propose several modifications to the method that aim at curing the size-dependent convergence behavior without significantly affecting the attractive features of the original method. The comparison with an auxiliary space preconditioner, a state-of-the-art solver for the considered problems, further indicates that both methods typically require a comparable amount of work to solve a given discretized problem but that the proposed approach requires less memory., SCOPUS: ar.j, info:eu-repo/semantics/published

Published
2019

19. Revisiting aggregation-based multigrid for edge elements. ETNA - Electronic Transactions on Numerical Analysis

Author

Napov, Artem and Perrussel, Ronan

Subjects
algebraic multigrid, edge elements, preconditioning, aggregation,Mathematics, Physics and Space Research
Abstract

We consider a modification of the Reitzinger-Schöberl algebraic multigrid method for the iterative solution of the curl-curl boundary value problem discretized with edge elements. The Reitzinger-Schöberl method is attractive for its low memory requirements and moderate cost per iteration, but the number of iterations typically tends to increase with the problem size. Here we propose several modifications to the method that aim at curing the size-dependent convergence behavior without significantly affecting the attractive features of the original method. The comparison with an auxiliary space preconditioner, a state-of-the-art solver for the considered problems, further indicates that both methods typically require a comparable amount of work to solve a given discretized problem but that the proposed approach requires less memory.

Published
2019

20. Algebraic analysis of two-level multigrid methods for edge elements

Author

Napov, Artem, Perrussel, Ronan, Napov, Artem, and Perrussel, Ronan

Abstract

We present an algebraic analysis of two-level multigrid methods for the solution of linear systems arising from the discretization of the curl-curl boundary value problem with edge elements. The analysis is restricted to the singular compatible linear systems as obtained by setting to zero the contribution of the lowest order (mass) term in the associated partial differential equation. We use the analysis to show that for some discrete curl-curl problems, the convergence rate of some Reitzinger-Schöberl two-level multigrid variants is bounded independently of the mesh size and the problem peculiarities. This covers some discretizations on Cartesian grids, including problems with isotropic coefficients, anisotropic coefficients and/or stretched grids, and jumps in the coefficients, but also the discretizations on uniform unstructured simplex grids., SCOPUS: ar.j, info:eu-repo/semantics/published

Published
2019

24. Discontinuous Galerkin discretizations of optimized Schwarz methods for solving the time-harmonic Maxwell's equations

Author

El Bouajaji Mohamed, Dolean Victorita, Gander Martin J., Lanteri Stéphani, Perrussel Ronan, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Section de mathématiques [Genève], Université de Genève (UNIGE), Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media (NACHOS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Groupe de Recherche en Electromagnétisme (LAPLACE-GRE), LAboratoire PLasma et Conversion d'Energie (LAPLACE), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées, Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Université de Genève = University of Geneva (UNIGE), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)

Subjects
[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; We show in this paper how to properly discretize optimized Schwarz methods for the time-harmonic Maxwell's equations in two and three spatial dimensions using a discontinuous Galerkin (DG) method. Due to the multiple traces between elements in the DG formulation, it is not clear a priori how the more sophisticated transmission conditions in optimized Schwarz methods should be discretized, and the most natural approach, at convergence of the Schwarz method, does not lead to the monodomain DG solution, which implies that for such discretizations, the DG error estimates do not hold when the Schwarz method has converged. We present here a consistent discretization of the transmission conditions in the framework of a DG weak formulation, for which we prove that the multidomain and monodomain solutions for the Maxwell's equations are the same. We illustrate our results with several numerical experiments of propagation problems in homogeneous and heterogeneous media.

Published
2015

25. A stochastic collocation method combined with a reduced basis method to compute uncertainties in numerical dosimetry

Author

Drissaoui, Amine, Musy, François, Nicolas, Laurent, Perrussel, Ronan, Voyer, Damien, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon, Perrussel, Ronan, and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SPI.ELEC]Engineering Sciences [physics]/Electromagnetism, [SPI.ELEC] Engineering Sciences [physics]/Electromagnetism, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; In this paper, a reduced basis method is introduced to deal with a stochastic problem in a numerical dosimetry application in which the field solutions are computed using an iterative solver. More precisely, the computations already performed are used to build an initial guess for the iterative solver. It is shown that this approach reduces significantly the computational cost with the same accuracy.

Published
2011

26. Hybrid−mixed formulation for static−current flow problem compared with conventional formulation

Author

Carpentier, Anthony, Rondot, Loïc, Perrussel, Ronan, Rodriguez, Eric, Guerin, Christophe, Laboratoire de Génie Electrique de Grenoble (G2ELab), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS), Cedrat, CEDRAT, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and Perrussel, Ronan

Subjects
[SPI.NRJ]Engineering Sciences [physics]/Electric power, [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

International audience; The electric scalar potential formulation is traditionally used to determine the static-current flow. This formulation is not naturally compatible with the electric vector potential formulation (T-φ). This is explained by a calculation of current coming from the summation of static and eddy currents whose functional spaces are different. In this paper, we propose an alternative approach based on mixed elements to obtain the current densities in the space H(div) and compare them to the electric scalar potential formulation.

Published
2011

27. Biological cell submitted to a ns electrical pulse

Author

Burais, Noël, Buret, François, Faure, Nicolas, Nicolas, Laurent, Perrussel, Ronan, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), ANR-06-BLAN-0260,CEMIRBIO,Champ ElectroMagnétique Impulsionnel Rapide et BIOlogie(2006), Ampère, Publications, Perrussel, Ronan, and Programme 'blanc' - Champ ElectroMagnétique Impulsionnel Rapide et BIOlogie - - CEMIRBIO2006 - ANR-06-BLAN-0260 - BLANC - VALID

Subjects
[SPI.ELEC]Engineering Sciences [physics]/Electromagnetism, [SPI.ELEC] Engineering Sciences [physics]/Electromagnetism, [SPI.NRJ]Engineering Sciences [physics]/Electric power, axisymmetric formulation, asymptotic model, Bioelectric field computation, [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

4 pages. Submitted to IEEE.; This work tackles the development of numerical methods in order to study the influence of a nanosecond electrical pulse on the phenomena arising in a biological cell. Formulations employed are presented and applied to the observation of the sensitivity of an eukaryote cell to the orientation of the electric field.

Published
2008

28. Méthodes multiniveau algébriques pour les éléments d'arête. Application à l'électromagnétisme

Author

Perrussel , Ronan, Institut Camille Jordan [Villeurbanne] ( ICJ ), École Centrale de Lyon ( ECL ), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS ), Centre de génie électrique de Lyon ( CEGELY ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Centre National de la Recherche Scientifique ( CNRS ), Ecole Centrale de Lyon, Laurent Nicolas(laurent.nicolas@ec-lyon.fr), Perrussel, Ronan, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Centre de génie électrique de Lyon (CEGELY), and Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon)

Subjects
minimisation sous contraintes, méthodes multigrille algébriques, [ INFO.INFO-MO ] Computer Science [cs]/Modeling and Simulation, electromagnetism, éléments finis d'arête, resolution of linear systems, constrained minimisation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, algebraic multigrid methods, edge elements, résolution de systèmes linéaires, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, électromagnétisme
Abstract

The computation of the electric or magnetic field plays a key-role in the design of efficient communication tools, in the electromagnetic compatibility of electronic systems and also in the modelling of the interaction between the field and living tissues. This computation is frequently based on the discretisation of Maxwell's equations by the edge element method. Then, it leads to solve a linear system with a sparse but usually large matrix.The aim of this work is to introduce an algebraic multilevel method for solving linear systems coming from the edge element method. Indeed, iterative multilevel methods generate algorithms which are the most efficient for some classes of partial differential equations. These methods are founded in their geometric version on a hierarchy of nested meshes; however, for realistic applications, this hierarchy cannot be constructed and the levels are then required to be algebraically defined.Our algebraic strategy for defining the coarse levels is founded on the construction of nodal and edge coarse bases, which have to minimise an energy functional. This minimisation problem with constraint is solved by two techniques: for the first one Lagrange multipliers are used, for the second technique a sequence of flow problems in a graph is solved. Some numerical experiments illustrate the performances of the different versions of our method., Le calcul numérique du champ électrique ou magnétique intervient aussi bien dans la mise au point d'outils de communication performants que dans les problèmes de compatibilité électromagnétique des systèmes électriques ou de modélisation de l'interaction champ-vivant. Ce calcul est fréquemment fondé sur la discrétisation des équations de Maxwell par la méthode des éléments finis d'arête. Il conduit alors à la résolution d'un système linéaire creux mais généralement de grande taille.L'objectif de ce travail est de proposer une méthode multiniveau algébrique pour la résolution des systèmes linéaires issus d'une discrétisation par la méthode des éléments finis d'arête. En effet, les méthodes itératives multiniveau construisent des algorithmes qui s'avèrent être les plus performants pour certaines classes l'équations aux dérivées partielles. Ces méthodes s'appuient, dans leur version géométrique, sur une hiérarchie de maillages emboîtés. Cependant pour des applications réalistes cette hiérarchie ne peut pas toujours être construite et il faut définir algébriquement les différents niveaux.La stratégie algébrique de définition des niveaux grossiers que nous proposons repose sur la construction de fonctions grossières nodales et d'arête vérifiant une contrainte de compatibilité. En outre, les fonctions grossières d'arête doivent minimiser une fonctionnelle d'énergie. Ce problème de minimisation avec contrainte est résolu par deux techniques : l'une utilise les multiplicateurs de Lagrange, l'autre s'appuie sur la résolution d'une suite de problèmes de flot dans un graphe. Des expériences numériques illustrent les performances de différentes versions de notre méthode.

Published
2005

29. Modélisation et mesure des couplages en champ proche des composants de filtre CEM

Author

Zangui, Sanaa, Vincent, Benjamin, Perrussel, Ronan, Berger, Kévin, Clavel, Edith, Vollaire, Christian, Sartori, Carlos, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire de Génie Electrique de Grenoble (G2ELab), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS), Escola Politecnica da Universidade de Sao Paulo [Sao Paulo], Instituto de Pesquisas Energéticas e Nucleares [São Paulo] (IPEN/CNEN-SP), Comissão National de Energia Nuclear (CNEN)-Universidade de São Paulo (USP), LIA franco brésilien James Clerk Maxwell (CNRS-CNPq) (LIA817), and Garcia, Sylvie

Subjects
[SPI.NRJ]Engineering Sciences [physics]/Electric power, [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

National audience; EMC filters are increasingly integrated into power applications. To improve the filter performance it is important to model the electromagnetic interference between the components to optimize their positions. In this paper, a method is proposed to construct the equivalent model of the filter components. The proposed method is based on the multipolar expansion by representing the radiated emission of generic structures in a spherical reference (r, θ, φ). These models of the sources will be used to compute the mutual inductance between the components according to their geometric placement. Some results are presented illustrating our method

Published
2010

30. Equivalent source corresponding to radiated field of EMC filter components

Author

Zangui, Sanâa, Berger, Kévin, Vincent, Benjamin, Perrussel, Ronan, Clavel, Edith, Vollaire, Christian, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire de Génie Electrique de Grenoble (G2ELab), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS), and Berger, Kévin

Subjects
mutual inductance, filter, [SPI.ELEC]Engineering Sciences [physics]/Electromagnetism, source, [SPI.ELEC] Engineering Sciences [physics]/Electromagnetism, [SPI.NRJ]Engineering Sciences [physics]/Electric power, radiated field, multipolar expansion, [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

International audience; EMC Filters are increasingly integrated into power applications. To improve their performances it is important to model the electromagnetic interference between components to optimize their positions in the filter. In this paper, a method is proposed to construct the equivalent models of the component radiated field. The method proposed is based on the multipolar expansion, which provides us reduced models for the field radiated by generic structures. These models of the sources will be used to compute the mutual inductance between the components according to their geometrical placement.

Published
2010

31. CAPTEURS DE COMPOSANTES MULTIPOLAIRES POUR UNE CARACTERISATION EN CHAMP PROCHE : PREMIERS RESULATS EXPERIMENTAUX

Author

Vincent, Benjamin, Chadebec, Olivier, Schanen, Jean-Luc, Berger, Kévin, Perrussel, Ronan, Krähenbühl, Laurent, Vollaire, Christian, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire de Génie Electrique de Grenoble (G2ELab), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS), and Garcia, Sylvie

Subjects
[SPI.NRJ]Engineering Sciences [physics]/Electric power, [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

International audience; De nouveaux capteurs d'induction magnétique en champ proche sont proposés pour des applications en Compatibilité ElectroMagnétique (CEM) des convertisseurs de l'électronique de puissance. Leur principe s'appuie sur celui des bobines de la norme CISPR 16-1, dont la forme permet de n'être sensible qu'à certaines composantes du développement multipolaire de l'induction magnétique générée par la source. Les nouveaux contours améliorent cette capacité de filtrage spatiale. Deux jeux complets de capteurs ont été élaborés mais seul le second permet d'envisager la construction d'un capteur complet. Le principe de construction des contours des bobines est exposé ainsi que leur validation expérimentale.

Published
2010

34. MODELISATION DES COUPLAGES EN CHAMP PROCHE DES COMPOSANTS DE FILTRES CEM

Author

Zangui, Sanaa, Berger, Kévin, Vincent, Benjamin, Clavel, Edith, Perrussel, Ronan, Vollaire, Christian, Garcia, Sylvie, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire de Génie Electrique de Grenoble (G2ELab), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SPI.NRJ]Engineering Sciences [physics]/Electric power, [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

International audience; Les filtres CEM sont de plus en plus intégrés en électronique de puissance. Pour améliorer leurs performances, il est important de modéliser le couplage champ proche optimiser leur positionnement. Cet article présente une approche qui permet la construction des sources équivalentes du rayonnement en champ proche de composants de filtres CEM. La méthode proposée est basée sur le développement multipolaire, c'est-à-dire la représentation du rayonnement de structures génériques dans un repère sphérique (r,θ,φ). Ces sources équivalentes seront utilisées pour calculer l'inductance mutuelle entre les composants en fonction de leur placement géométrique.

Published
2010

35. Agglomeration-based algebraic multigrid for linear systems coming from edge-element discretizations

Author

Musy, François, Nicolas, Laurent, Perrussel, Ronan, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Ampère (AMPERE), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), and Ampère, Publications

Subjects
[SPI.NRJ]Engineering Sciences [physics]/Electric power, [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

International audience; An algebraic multigrid algorithm based on element agglomeration is proposed for linear systems coming from edgeelement discretizations. The edge prolongation operator satisfies commutativity and energy-minimization properties. Robustness is illustrated on 2D numerical examples

Published
2009

36. Identification de sources multipolaires équivalentes par filtrage spatial

Author

Vincent, Benjamin, Chadebec, Olivier, Schanen, Jean-Luc, Berger, Kévin, Krähenbühl, Laurent, Perrussel, Ronan, Laboratoire de Génie Electrique de Grenoble (G2ELab), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and Berger, Kévin

Subjects
[PHYS.COND.CM-S]Physics [physics]/Condensed Matter [cond-mat]/Superconductivity [cond-mat.supr-con], [SPI.ELEC]Engineering Sciences [physics]/Electromagnetism, [SPI.ELEC] Engineering Sciences [physics]/Electromagnetism, [SPI.NRJ]Engineering Sciences [physics]/Electric power, [PHYS.COND.CM-S] Physics [physics]/Condensed Matter [cond-mat]/Superconductivity [cond-mat.supr-con], [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

International audience; De nouveaux capteurs d'induction magnétique en champ proche, dédiés aux études de Compatibilité Electromagnétique, sont proposés sur le principe des spires de la norme CISPR16-1. La forme des bobines proposées leur permet de n'être sensibles qu'à certaines composantes multipolaires du champ, ce qui réalise un filtrage spatial. Après une description de la méthode de synthèse de ces contours, une validation numérique est exposée.

Published
2008

37. Comparison between finite difference and finite element methods: application to biological cell exposure

Author

Burais, Noël, Buret, François, Faure, Nicolas, Nicolas, Laurent, Perrussel, Ronan, Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and Ampère, Publications

Subjects
education, [SPI.NRJ]Engineering Sciences [physics]/Electric power, health care economics and organizations, [SPI.NRJ] Engineering Sciences [physics]/Electric power
Abstract

International audience; The finite element and finite difference methods are compared for the modelling of a biological cell exposed to an electric pulse.

Published
2008

41. Krylov-based algebraic multigrid for edge elements

Author

Musy, François, Napov, Artem, Notay, Yvan, Perrussel, Ronan, Scorretti, Riccardo, Musy, François, Napov, Artem, Notay, Yvan, Perrussel, Ronan, and Scorretti, Riccardo

Abstract

http://hal.archives-ouvertes.fr/hal-00412347/fr, info:eu-repo/semantics/published

Published
2009

42. Eddy Currents and Corner Singularities

Author

Buret, François, primary, Dauge, Monique, additional, Dular, Patrick, additional, Krahenbuhl, Laurent, additional, Peron, Victor, additional, Perrussel, Ronan, additional, Poignard, Clair, additional, and Voyer, Damien, additional

Published
2012
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