98 results on '"Péron, Victor"'
Search Results
2. On Ventcel-type transmission conditions for a Helmholtz problem with a non-uniform thin layer
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Boutarene, Khaled El-Ghaouti, Galleze, Sami, and Péron, Victor
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- 2024
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3. The airfoil integral equation over disjoint intervals: analytic solutions and asymptotic expansions
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Farina, Leandro, Ferreira, Marcos R. S., and Péron, Victor
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- 2024
- Full Text
- View/download PDF
4. Efficient asymptotic models for axisymmetric eddy current problems in linear ferromagnetic materials
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Yafi, Dima Abou El Nasser El and Péron, Victor
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Mathematics - Numerical Analysis - Abstract
The problem under consideration is that of time-harmonic eddy current problems in linear ferromagnetic materials surrounded by a dielectric medium with a smooth common interface. Assuming axisymmetric geometries and orthoradial axisymmetric data, we construct an efficient multiscale expansion for the orthoradial solution that provides reduced computational costs. We investigate numerically the accuracy of the approach using an analytical procedure and infinite cylinders as well. It results that the computation of two asymptotics is sufficient to ensure accurate solutions in the case of low frequencies., Comment: 24 pages, 12 figures
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- 2023
5. Wentzel--Kramers--Brillouin Expansions and Generalized Impedance Transmission Conditions for Thin-Layer Problems in Electromagnetism with Application to Biological Cells
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Péron, Victor
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Mathematics - Numerical Analysis ,35C20, 35J25, 35Q60, 35R05, 41A60, 58J37 - Abstract
In this work we derive a WKB expansion for the electromagnetic fields solution of the time-harmonic Maxwell equations set in a domain with a thin layer. As a by-product of this expansion we obtain new second order asymptotic models with generalized impedance transmission conditions that turn out to depend on the mean curvature of the boundary of the subdomain surrounded by the thin layer. We show that these models can be easily integrated in finite element methods by developing mixed variational formulations. One application of this work concerns the computation of the electromagnetic field in biological cells.
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- 2022
6. Asymptotic Study for Stokes-Brinkman model with jump embedded transmission conditions
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Angot, Philippe, Carbou, Gilles, and Péron, Victor
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Mathematics - Analysis of PDEs - Abstract
In this paper, one considers the coupling of a Brinkman model and Stokes equations with jump embedded transmission conditions. In this model, one assumes that the viscosity in the porous region is very small. Then we derive a Wentzel--Kramers--Brillouin (WKB) expansion in power series of the square root of this small parameter for the velocity and the pressure which are solution of the transmission problem. This WKB expansion is justified rigorously by proving uniform errors estimates.
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- 2022
7. Corner asymptotics of the magnetic potential in the eddy-current model
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Dauge, Monique, Dular, Patrick, Krähenbühl, Laurent, Péron, Victor, Perrussel, Ronan, and Poignard, Clair
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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.
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- 2022
- Full Text
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8. Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer
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Péron, Victor
- Subjects
Mathematics - Numerical Analysis ,Mathematics - Analysis of PDEs ,35C20, 35J25, 41A60, 74F10 - Abstract
We present equivalent conditions and asymptotic models for the diffraction problem of elastic and acoustic waves in a solid medium surrounded by a thin layer of fluid medium. Due to the thinness of the layer with respect to the wavelength, this problem is well suited for the notion of equivalent conditions and the effect of the fluid medium on the solid is as a first approximation local. We derive and validate equivalent conditions up to the fourth order for the elastic displacement. These conditions approximate the acoustic waves which propagate in the fluid region. This approach leads to solve only elastic equations. The construction of equivalent conditions is based on a multiscale expansion in power series of the thickness of the layer for the solution of the transmission problem.
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- 2022
9. On the influence of the geometry on skin effect in electromagnetism
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Caloz, Gabriel, Dauge, Monique, Faou, Erwan, and Péron, Victor
- Subjects
Mathematics - Analysis of PDEs ,Mathematics - Numerical Analysis - Abstract
We consider the equations of electromagnetism set on a domain made of a dielectric and a conductor subdomain in a regime where the conductivity is large. Assuming smoothness for the dielectric--conductor interface, relying on recent works we prove that the solution of the Maxwell equations admits a multiscale asymptotic expansion with profile terms rapidly decaying inside the conductor. This skin effect is measured by introducing a skin depth function that turns out to depend on the mean curvature of the boundary of the conductor. We then confirm these asymptotic results by numerical experiments in various axisymmetric configurations. We also investigate numerically the case of a nonsmooth interface, namely a cylindrical conductor.
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- 2022
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10. Efficient asymptotic models for axisymmetric eddy current problems in linear ferromagnetic materials
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Abou El Nasser El Yafi, Dima and Péron, Victor
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- 2023
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11. Semi-analytical solutions for the problem of the electric potential set in a borehole with a highly conductive casing
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Erdozain, Aralar, Muga, Ignacio, Péron, Victor, and Pinochet, Gabriel
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- 2022
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12. Equivalent multipolar point-source modeling of small spheres for fast and accurate electromagnetic wave scattering computations
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Labat, Justine, Péron, Victor, and Tordeux, Sébastien
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- 2020
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13. On a magnetic skin effect in eddy current problems: the magnetic potential in magnetically soft materials
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Péron, Victor and Poignard, Clair
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- 2021
- Full Text
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14. Boundary element method for 3D conductive thin layer in eddy current problems
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Issa, Mohammad, Poirier, Jean-René, Perrussel, Ronan, Chadebec, Olivier, and Péron, Victor
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- 2019
- Full Text
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15. Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism
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Caloz, Gabriel, Dauge, Monique, and Péron, Victor
- Subjects
Mathematics - Numerical Analysis - Abstract
In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work, the interface between the two subdomains is supposed to be Lipschitz. We first study a scalar transmission problem which is handled through a converging asymptotic series. Then we derive uniform a priori estimates for Maxwell transmission problem set on a domain made up of a dielectric and a highly conducting material. The technique is based on an appropriate decomposition of the electric field, whose gradient part is estimated thanks to the first part. As an application, we develop an argument for the convergence of an asymptotic expansion as the conductivity tends to infinity.
- Published
- 2009
16. The airfoil equation on near disjoint intervals: Approximate models and polynomial solutions
- Author
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Farina, Leandro, Ferreira, Marcos R.S., and Péron, Victor
- Published
- 2016
- Full Text
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17. Hypersingular integral equations over a disc: Convergence of a spectral method and connection with Tranter’s method
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Farina, Leandro, Martin, P.A., and Péron, Victor
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- 2014
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18. Numerical study of the magnetic skin effect: Efficient parameterization of 2D surface‐impedance solutions for linear ferromagnetic materials
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Abou El Nasser El Yafi, Dima, primary, Péron, Victor, additional, Perrussel, Ronan, additional, and Krähenbühl, Laurent, additional
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- 2022
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19. Numerical study of the magnetic skin effect: Efficient parameterization of 2D surface‐impedance solutions for linear ferromagnetic materials.
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Abou El Nasser El Yafi, Dima, Péron, Victor, Perrussel, Ronan, and Krähenbühl, Laurent
- Subjects
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SKIN effect , *FERROMAGNETIC materials , *FINITE element method , *MAGNETIC permeability , *PARAMETERIZATION - Abstract
This work presents an efficient method based on asymptotic models in order to solve numerically eddy current problems in a bi‐dimensional setting with a high contrast of linear relative magnetic permeability μr ≫ 1 between a conductor and a dielectric subdomain. We describe a magnetic skin effect by deriving a multiscale expansion for the magnetic potential in power series of a small parameter δ which represents the skin depth. We make explicit the first asymptotics up to the order three. Some numerical results based on the finite element method will be presented to illustrate the magnetic skin effect and to validate the performance of the proposed asymptotic models in the dielectric medium. We confirm that the proposed asymptotics provide reduced computational costs for a wide range of physical parameters introduced in our problem. [ABSTRACT FROM AUTHOR]
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- 2023
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20. A NUMERICAL STUDY OF THE MAGNETIC SKIN EFFECT: EFFICIENT PARAMETRIZATION OF 2D SURFACE-IMPEDANCE SOLUTION FOR LINEAR FERROMAGNETIC MATERIALS
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Abou El Nasser El Yafi, Dima, Péron, Victor, Perrussel, Ronan, Krähenbühl, Laurent, Laboratoire de Mathématiques appliquées de Pau (LMAP), Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA), E2S UPPA, Centre National de la Recherche Scientifique (CNRS), Université de Pau et des Pays de l'Adour (UPPA), 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, Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), 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), and 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)
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Eddy current problems ,Finite element method ,Asymptotic expansions ,Ferromagnetic materials ,Impedance boundary conditions ,Magnetic potential ,[MATH]Mathematics [math] - Abstract
This work presents an efficient method based on asymptotic models in order to solve numerically eddy current problems in a bi-dimensional setting with a high contrast of linear relative magnetic permeability mu_r between a conductor and a dielectric subdomain. We describe a magnetic skin effect by deriving a multiscale expansion for the magnetic potential in power series of a small parameter delta which represents the skin depth. We make explicit the first asymptotics up to the order three. Some numerical results based on the finite element method will be presented to illustrate the magnetic skin effect and to validate the performance of the proposed asymptotic models in the dielectric medium. We confirm that the proposed asymptotics provide reduced computational costs for a wide range of the physical parameters introduced in our problem.
- Published
- 2021
21. On the influence of the geometry on skin effect in electromagnetism
- Author
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Caloz, Gabriel, Dauge, Monique, Faou, Erwan, and Péron, Victor
- Published
- 2011
- Full Text
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22. Asymptotic Models for Ferromagnetic Materials in Eddy Current Problem
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Abou El Nasser El Yafi, Dima, Péron, Victor, Perrussel, Ronan, Université de Pau et des Pays de l'Adour (UPPA), E2S UPPA, Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), 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, 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), and ABOU EL NASSER EL YAFI, Dima
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[INFO]Computer Science [cs] ,[INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation ,[INFO] Computer Science [cs] ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation - Abstract
International audience; The eddy current problem has crucial applications in the industrial field such asinductive heating or braking of heavy vehicles. In this context, we intend toanalyze the eddy current problem for the electromagnetic field in magneticallysoft materials. These materials are used for the cores of transformers in order toreduce the energy losses resulting from the alternating currents. The problem under consideration lies in two highly heterogeneous materialswith a common interface: we are interested to study the electromagnetic field ina soft magnetic conducting body with a high constant permeability mu = mu−, embeddedin a magnetic dielectric medium with a constant permeability mu=mu+, in a three-dimensionalsetting. Therefore, we propose to investigate the behavior of the electromagnetic field when themagnetic permeability is “dominant” that is the ferromagnetic case.However, in the ferromagnetic materials, we may have a small skin depth andthe amplitude of the magnetic field decays rapidly with depth inside themagnetic conducting domain. As a result, the numerical simulation of such aproblem seems challenging although prohibitive. In order to overcome thisdifficulty, we introduce for instance a small parameter epsilon, then we developan asymptotic approach based on a multiscale expansion. This asymptotic method wasalso applied previously for highly conductive nonmagnetic materials in eddy current problem.Therefore, we derive asymptotic models that reflect the skin effect and can be solved numericallyby using a coarse mesh.The aim of our present work is twofold. First, we derive an asymptoticexpansion of the electromagnetic field as the parameter epsilon tends to zero whenthe surface of the conducting body is smooth. Then, as an application, wemeasure the magnetic skin effect by presenting the asymptotic behavior of thecharacteristic depth. Finally, we compare the latter result with the previous workcorresponding to the skin effect in a bidimensional eddy current problem, whenthe contrast of permeability is predominant
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- 2021
23. Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism
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Caloz, Gabriel, Dauge, Monique, and Péron, Victor
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- 2010
- Full Text
- View/download PDF
24. Asymptotic models for the multiple electromagnetic wave scattering problem by small obstacles
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Labat, Justine, Péron, Victor, Tordeux, Sébastien, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
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[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,[MATH]Mathematics [math] ,ComputingMilieux_MISCELLANEOUS ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience
- Published
- 2019
25. The multiple electromagnetic wave scattering by small spheres
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Labat, Justine, Péron, Victor, Tordeux, Sébastien, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), and Université de Pau et des Pays de l'Adour (UPPA)
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[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,[MATH]Mathematics [math] ,ComputingMilieux_MISCELLANEOUS ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience
- Published
- 2018
26. Asymptotic modeling of the multiple electromagnetic wave scattering by small spheres
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Labat, Justine, Péron, Victor, Tordeux, Sébastien, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
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[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,[MATH]Mathematics [math] ,ComputingMilieux_MISCELLANEOUS - Abstract
International audience
- Published
- 2018
27. Foldy-Lax Model for the Scattering Problem in Electromagnetism
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Labat, Justine, Péron, Victor, Tordeux, Sébastien, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université de Pau et des Pays de l'Adour (UPPA)
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[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,[MATH]Mathematics [math] ,ComputingMilieux_MISCELLANEOUS ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience
- Published
- 2018
28. Asymptotic Modeling of the Electromagnetic Scattering by Small Spheres Perfectly Conducting
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Labat, Justine, Péron, Victor, Tordeux, Sébastien, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Pau et des Pays de l'Adour (UPPA), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Université de Pau et des Pays de l'Adour, Inria Bordeaux Sud-Ouest, and LMAP UMR CNRS 5142
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Développements asymptotiques ,Asymptotic expansions ,Reduced models ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,[MATH]Mathematics [math] ,Équations de Maxwell ,Modèles réduits ,Maxwell’s equations ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Published
- 2018
29. Asymptotic Models and Impedance Conditions for Highly Conductive Sheets in the Time-Harmonic Eddy Current Model
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Péron, Victor, primary
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- 2019
- Full Text
- View/download PDF
30. Asymptotic Models for Acoustic, Elastic and Electromagnetic Media. Corner and Edge Asymptotics for Elliptic Systems
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Péron, Victor, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Université de Pau et des Pays de l'Adour, and Grégory Vial
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Asymptotic Analysis ,[SPI.NRJ]Engineering Sciences [physics]/Electric power ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Mathematical modeling ,Analyse asymptotique ,Modélisation mathématique ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
Nous présentons quelques contributions autour de l'analyse asymptotique et l'étude des singularités de solutions d'équations aux dérivées partielles de type elliptique, de l'analyse numérique et du calcul scientifique. Ces travaux sont motivés par des applications physiques, principalement en électromagnétisme (calcul de courants de Foucault, modélisation de cellules biologiques), en mécanique et en acoustique (sismologie, diffraction). Nous développons des conditions d'impédance, pour les équations de Maxwell harmoniques, adaptées à des interfaces de matériaux fortement conducteurs. Nous présentons aussi des conditions aux limites équivalentes adaptées à des milieux minces à l'échelle terrestre pour des couplages élasto-acoustiques. Nous développons des méthodes asymptotiques et numériques qui permettent de résoudre des problèmes de transmission en présence de singularités de coins (problèmes de courant de Foucault). Nous développons aussi ce type de méthodes afin de déterminer des développements asymptotiques de fonctions harmoniques au voisinage de singularités d'arêtes.; We develop asymptotic methods to solve problems arising in the context of acoustic, elastic or electromagnetic wave propagation phenomena and which involve small parameters (boundary layer problems, thin-layer problems, problems with small defects). Such phenomena are eventually described with multi-scale expansions and asymptotic models. Reduced models have been implemented in Finite Element codes in order to analyse numerically their properties. Several works are presented in a first part which is divided into two chapters. The first chapter is devoted to thin-layer transmission problems in acoustic and elastic media. This work enters into the scope of the HPC GA project (High Performance Computing for Geophysics Applications). The second chapter concerns transmission problems of electromagnetic waves across thin layers with high conductivities. This part is complemented with an asymptotic study on the accuracy of different approximations of the electromagnetic field for thin-layer transmission problems, Appendix A. In the context of fluid flow modeling in complex media combining porous and fluid regions with free flow and a high contrast of viscosities, we develop a WKB expansion to solve a singular perturbation problem, Appendix B. Corner and edge singularities on interfaces may increase the level of difficulty in the analysis of elliptic problems in comparison with smooth interfaces. We develop asymptotic technics to determine corner and edge asymptotics in elliptic systems for several applications in electromagnetism and in elasticity. Eddy current problems have been addressed in the presence of a corner singularity on an interface (dielectric/conductor) and crack problems have been addressed in the context of elasticity. The asymptotic analysis of such a problem relies on the determination of a (Kondrat'ev type) singular expansion which is a series of asymptotics defined in a vicinity of a corner or edge singularity. This expansion generalizes the Taylor one which holds in smooth domains. The notion of asymptotics involve two ingredients which are the singular coefficients and the singular functions (also called the singularities). The singularities are associated with singular exponents and may be determined with the Mellin analysis. The singular coefficients may be extracted with numerical methods such as the quasi dual function method (QDFM) which requires the knowledge of dual singularities. Several works related to these problems are presented in a second part which is divided into two chapters. Chapter 3 is mainly devoted to the determination of corner asymptotics of the magnetic potential in the eddy-current model. The first terms of a multi-scale expansion of the magnetic potential are also introduced to tackle the magneto-harmonic problem as the skin depth goes to zero. As an application, a modified (Leontovich) impedance boundary condition close to a corner singularity has been proposed. Chapter 4 is devoted to the notion of edge asymptotics for the Laplace operator. We make the focus on the extraction of edge flux intensity factors (EFIFs) associated with the integer eigenvalues for the Laplace operator over a 3-D domain with a straight crack. The dual singularities are determined and the QDFM has been extended for the extraction of EFIFs. Spectral methods and polynomial solutions are developed to solve hypersingular integral equations over a disc and the airfoil equation (with a Cauchy type of singularity) over close disjoint intervals, Appendix C.
- Published
- 2017
31. Impedance Transmission Conditions for the Electric Potential across a Highly Conductive Casing
- Author
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Barucq, Hélène, Erdozain, Aralar, Péron, Victor, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), and Inria Bordeaux Sud-Ouest
- Subjects
Conductivity ,Asymptotic Models ,Forage ,Resistivity ,Potentiel Électrique ,Casing ,Conductivité ,Borehole ,Modèles Asymptotiques ,Conditions d'Impedance ,Electric Potentential ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Impedance Conditions ,[MATH]Mathematics [math] ,Résistivité - Published
- 2016
32. Equivalent boundary conditions for acoustic media with exponential densities. Application to the atmosphere in helioseismology
- Author
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Chabassier, Juliette, Duruflé, Marc, Péron, Victor, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), 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), Inria Bordeaux Sud-Ouest, Université de Pau et des Pays de l'Adour, and Université de Bordeaux
- Subjects
Multiscale Expansions ,Equivalent Boundary Conditions ,Numerical Methods for Helioseismology ,Méthodes Numériques pour l'Héliosismologie ,[INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA] ,Conditions aux Limites Equivalentes ,Analyse Asymptotique - Published
- 2016
33. Description of a boundary layer phenomenon in acoustic media with a multi-scale expansion. Application
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Barucq, Hélène, Chabassier, Juliette, Duruflé, Marc, Péron, Victor, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
- Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience; We consider a transmission problem for the propagation of an acoustic wave in heterogeneous media in time-harmonic regime. The domain of interest represents the sun and its atmosphere. This problem involves a large parameter $\alpha$ which corresponds to the exponential decay rate of the density inside the atmosphere. In this framework a boundary layer phenomenon occurs inside the atmosphere. There are several similarities with the skin effect in electromagnetism. We describe the boundary layer phenomenon with a multi-scale expansion in power series of $\alpha −1$. As an application we derive approximate boundary conditions. This approach leads to solve only equations set inside the sun. Numerical results illustrate the accuracy of the approximate models.
- Published
- 2016
34. The Laplace equation in 3-D domains with cracks: Dual shadows with log terms and extraction of corresponding edge flux intensity functions
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Shannon, Samuel, Péron, Victor, Yosibash, Zohar, Department of Mechanical Engineering [Beer-Sheva], Ben-Gurion University of the Negev (BGU), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Israel Science Foundation (grants No. 444/10 and 593/14) and INRIA
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Logarithmic singularities ,edge flux/stress intensity functions ,3-D singularities ,dual eigenvalues ,[MATH]Mathematics [math] ,quasi-dual function method - Abstract
International audience; The singular solution of the Laplace equation with a straight-crack is represented by a series of eigenpairs, shadows and their associated edge flux intensity functions (EFIFs). We address the computation of the EFIFs associated with the integer eigenvalues by the quasi dual function method (QDFM).The QDFM is based on the dual eigenpairs and shadows, and we show that the dual shadows associated with the integer eigenvalues contain logarithmic terms. These are then used with the QDFM to extract EFIFs from p-version finite element solutions. Numerical examples are provided. Dedicated to the 65th birthday of prof. Martin Costabel.
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- 2016
35. Singular asymptotic solution along an elliptical edge for the Laplace equation in 3-D
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Shannon, Samuel, Peron, Victor, and Yosibash, Zohar
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- 2015
- Full Text
- View/download PDF
36. Asymptotic expansion for the magnetic potential in the eddy current problem : the ferromagnetic case
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Péron, Victor, Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)
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[SPI.ELEC]Engineering Sciences [physics]/Electromagnetism ,[MATH]Mathematics [math] ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Published
- 2015
37. Equivalent absorbing boundary conditions for heterogeneous acoustic media
- Author
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Castro, Manuela, Diaz, Julien, Péron, Victor, Departamento de Matemática Pura e Aplicada [Porto Alegre] (UFRGS), Universidade Federal do Rio Grande do Sul [Porto Alegre] (UFRGS), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Pau et des Pays de l'Adour (UPPA), and Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)
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ondas acústicas ,lcsh:Mathematics ,heterogeneous media ,acoustic waves ,lcsh:QA1-939 ,artificial boundaries ,condições de contorno equivalentes ,Propagação de ondas ,meio heterogêneo ,equivalent boundary conditions ,computational wave propagation ,QA1-939 ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Computationalwave propagation ,Mathematics ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] ,contornos artificiais - Abstract
In this work, we derive high order Equivalent Absorbing Boundary Conditions EABCs that model the propagation of waves in semi-infinite bilayered acoustic media. Our motivation is to restrict the computational domain in the simulation of seismic waves that are propagated from the earth and transmitted to the stratified heterogeneous media composed by ocean and atmosphere. These EABCs are adapted to Hagstrom-Warburton ABCs and appear as first and second order of approximation with respect to a small parameter involved in a multiscale expansion. Computational tests illustrate the accuracy of the first approximate model with respect to the small parameter. Partindo de uma modelagem no domínio de frequências, utilizamos condições de contorno artificiais de Higdon e aproximações assintóticas para obter condições de contorno equivalentes que viabilizem a redução do domínio computacional para a simulação da propagação de ondas em meios acústicos heterogêneos. A motivação para este trabalho é a obtenção de condições de contorno artificiais e aproximadas para a simulação da propagação de ondas sísmicas, oriundas do interior da terra e transmitidas ao meio acústico heterogêneo composto pelos oceanos e pela atmosfera.
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- 2014
38. Mathematical modeling of electromagnetic phenomena in high contrast media
- Author
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Péron, Victor, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Université Rennes 1, Monique Dauge(monique.dauge@univ-rennes1.fr), Péron, Victor, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)
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electromagnetic waves ,thin layer ,[ MATH ] Mathematics [math] ,électroporation ,high conductivity ,numerical analysis ,couche limite ,couche mince ,[MATH] Mathematics [math] ,electroporation process ,analyse numérique ,boundary layer ,effet de peau ,skin effect ,analyse asymptotique ,asymptotic analysis ,Maxwell equations ,haute conductivité ,équations de Maxwell ,[MATH]Mathematics [math] ,ondes électromagnétiques - Abstract
This work consists in the study of transmission problems of electromagnetic waves in high contrast media, like a highly conducting body embedded in an insulating medium. We perform an accurate analysis of the skin effect by the way of the asymptotic analysis and numerical simulations. We derive a scaled asymptotic expansion in the three dimensionnal cae of the harmonic Maxwell equations with high conductivity. We prove uniform estimates with respect to the high conductivity in polyhedral domains with Lipschitz boundaries. These estimates motive the study of a scalar transmission problem, in which case a priori estimates are obtained by the way of an asymptotic expansion. Numerical simulations in axisymetric geometry highlight the skin effect and show the expansion accuracy.Next, we study the behavior of the electromagnetic field in a biological cell modelized by a medium surrounded by a thin layer and embedded in an ambient medium. We derive approximate transmission conditions in order to replace the membrane by these conditions on the boundary of the interior domain., Ce travail est consacré à l'étude d'un problème de transmission d'ondes électromagnétiques dans des matériaux fortement conducteurs entourés d'un matériau diélectrique isolant. On analyse finement le phénomène de l'effet de peau à l'aide de l'analyse asymptotique et de la simulation numérique. On calcule un développement asymptotique multi-échelle à haute conductivité des solutions des équations de Maxwell tridimensionnelles en régime harmonique. Pour valider ce développement, on établit des estimations uniformes par sous-domaines des solutions de ces équations pour une conductivité assez élevée. Ces estimations ont motivé une étude préliminaire d'un problème de transmission scalaire pour lequel des estimations a priori sont démontrées grâce à la convergence normale d'un développement asymptotique. L'accord des formules théoriques avec les calculs numériques est remarquable et met en évidence l'influence de la géométrie de l'interface dans le phénomène de l'effet de peau.D'autre part, on étudie le comportement du champ électromagnétique dans une cellule biologique modélisée par un milieu entouré d'une couche mince et plongée dans un milieu ambiant. On calcule des conditions de transmission approchées sur le bord du domaine intérieur équivalentes à la couche mince.
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- 2009
39. Skin Effect Description in Electromagnetism with a Multiscaled Asymptotic Expansion
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Caloz , Gabriel, Dauge , Monique, Faou , Erwan, Péron , Victor, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Invariant Preserving SOlvers (IPSO), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-AGROCAMPUS OUEST, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Inria Rennes – Bretagne Atlantique, Péron, Victor, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Invariant Preserving SOlvers ( IPSO ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Rennes – Bretagne Atlantique, and Institut National de Recherche en Informatique et en Automatique ( Inria )
- Subjects
[ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA] ,[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience; We study a transmission problem in high contrast media. The three-dimensional case of the Maxwell equations in harmonic regime is considered. We derive an asymptotic expansion with respect to a small parameter related to high conductivity. This expansion is theoretically justified at any order. Numerical simulations in axisymmetric geometry highlight the skin effect and the expansion accuracy.
- Published
- 2009
40. Asymptotic delta-Parameterization of Surface-Impedance Solutions
- Author
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Krähenbühl, Laurent, Dular, Patrick, Péron, Victor, Perrusel, Ronan, Poignard, Clair, and Sabariego, Ruth
- Abstract
The surface impedance methods are among the most efficient for solving time-harmonic eddy-current problems with a small penetration depth. When the solution is required for a wide range of frequencies (or material conductivities) the standard approach leads to the solution of a complex-valued problem for each frequency (or conductivity). Hereafter we introduce a close method, parametrized by the skin depth (delta), based on a formal asymptotic expansion. It provides accurate results with a reduced computational cost for a wide range of delta values. ispartof: Biennial IEEE Conference on Electromagnetic Field Computation location:Annecy status: published
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- 2014
41. Equivalent Robin boundary conditions for acoustic and elastic media
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Diaz, Julien, primary and Péron, Victor, additional
- Published
- 2016
- Full Text
- View/download PDF
42. Asymptotic study for Stokes–Brinkman model with jump embedded transmission conditions
- Author
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Angot, Philippe, primary, Carbou, Gilles, additional, and Péron, Victor, additional
- Published
- 2016
- Full Text
- View/download PDF
43. Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer
- Author
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Péron, Victor, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, and European Project: 295217,EC:FP7:PEOPLE,FP7-PEOPLE-2011-IRSES,HPC-GA(2012)
- Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
In this paper we present equivalent conditions and asymptotic models for the diffraction problem of elasto-acoustic waves in a solid medium surrounded by a thin layer of fluid medium. This problem is well suited for the notion of equivalent conditions : since the thickness of the layer is small with respect to the wavelength, the effect of the fluid medium on the solid is as a first approximation local. We derive and validate equivalent conditions up to the third order for the elastic displacement. These conditions approximate the acoustic waves which propagate in the fluid region. This approach leads us to solve only elastic equations. The construction of equivalent conditions is based on a multiscale expansion in power series of the thickness of the layer for the solution of the transmission problem.; Dans ce document, on présente des conditions d'impédances ainsi que des modèles asymptotiques adaptés à des problèmes de transmission pour des couplages élasto-acoustiques dans des milieux avec couche mince acoustique. Ce type de problème est bien posé pour la notion de conditions équivalentes car la faible épaisseur de la couche assure que l'effet acoustique sur la déformation élastique est en première approximation locale. On introduit et justifie rigoureusement des conditions équivalentes adaptées à une telle couche mince. Cette méthode permet d'approcher la solution du problème couplé par celle d'un problème aux limites avec une condition d'impédance, l'erreur d'approximation est contrôlée par rapport à l'épaisseur de la couche.
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- 2013
44. Construction and Analysis of Equivalent Models for Fluid-Structure Coupling with a Thin Layer
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Péron, Victor, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
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ComputingMilieux_MISCELLANEOUS ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience
- Published
- 2012
45. On the Influence of the Geometry on Skin Effect in Electromagnetism
- Author
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Péron, Victor, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
- Subjects
ComputingMilieux_MISCELLANEOUS ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience
- Published
- 2010
46. Modélisation de phénomènes électromagnétiques dans des milieux à fort contraste
- Author
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PÉRON, Victor, Modélisation, contrôle et calcul (MC2), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), and LATP, Université de Provence
- Subjects
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience; Je présente d'abord un problème de transmission d'ondes électromagnétiques dans un matériau fortement conducteur entouré d'un matériau isolant. Dans ce contexte, l'effet de peau décrit la décroissance rapide du champ électromagnétique près de la surface du conducteur. Je décris ce phénomène par un développement asymptotique multi-échelle à haute conductivité des solutions des équations de Maxwell pour une interface régulière. Ce développement est justifié par des estimations uniformes à haute conductivité. Il met en évidence l'influence de la courbure moyenne de la surface du conducteur sur l'effet de peau. J'illustre ces résultats par des calculs éléments finis de haut degré. Je m'intéresse ensuite au phénomène d'électroporation (ETP) à l'échelle cellulaire qui reflète la formation de pores à travers la membrane plasmique sous l'effet d'un champ électrique. Ce phénomène est fondamental dans la compréhension et la modélisation de l'électrochimiothérapie antitumorale. Je présente un modèle d'ETP prenant en compte les interactions électromagnétiques afin d'affiner les modèles actuels pour le potentiel électrique développés au sein de l'EPI MC2. L'idée consiste à mimer le champ dans la membrane via une condition de transmission approchée sur le bord du cytoplasme, calculée par un développement asymptotique du champ électromagnétique. Des calculs éléments finis 3D (code Montjoie) illustrent la précision du modèle approché.
- Published
- 2010
47. Sur l'effet de peau en électromagnétisme
- Author
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Péron, Victor, Modélisation, contrôle et calcul (MC2), Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Published
- 2010
48. Skin Effect in Electromagnetism and Asymptotic Behaviour of Skin Depth for High Conductivity
- Author
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PÉRON, Victor, Modélisation, contrôle et calcul (MC2), Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Published
- 2010
49. Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer
- Author
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Péron, Victor, primary
- Published
- 2014
- Full Text
- View/download PDF
50. Progressive eddy current modeling via a finite element subproblem method
- Author
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Dular, Patrick, primary, Péron, Victor, additional, Krähenbühl, Laurent, additional, and Geuzaine, Christophe, additional
- Published
- 2014
- Full Text
- View/download PDF
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