Page de Éliane Bécache

Éliane
Bécache 		Chercheur
Dir. Adj. EDMH
Chargé de Recherche
H.D.R. depuis 2003


Page personnelle
INRIA
bureau 2.2.26
Tél : (0) 18 187 2084

Recherches

    Analyse mathématique et numérique d'EDP pour la propagation d'ondes transitoires ainsi que de méthodes d'approximation pour les résoudre : domaines fictifs, éléments finis mixtes, approximations paraxiales, potentiels retardés...
    Résolution en domaine non borné : CLA (Conditions aux Limites Absorbantes), couches absorbantes parfaitement adaptées (PML) en régime transitoire et fréquentiel.

Enseignements

  • Cours Résolution des problèmes de diffraction par équations intégrales, 3ème année à l'ENSTA et M2, Master AMS.
  • TD/TP Eléments Finis I, ANN201, 2ème année à l'ENSTA et master M1 MathApp Orsay.
  • Cours et TD/TP Eléments Finis II, ANN202, 2ème année à l'ENSTA et master M1 MathApp Orsay.
  • TD Variable Complexe, MA104, 1ère année à l'ENSTA.
  • TD Introduction à la discrétisation des équations aux dérivées partielles, MA103, 1ère année à l'ENSTA.

Articles (revue avec comité de lecture)

É. Bécache, A.-S. Bonnet-BenDhia, S. Fliss, A. Tonnoir
The Half-Space Matching method for elastodynamic scattering problems in unbounded domains (2023)
Journal of Computational Physics - vol. 490 
É. Bécache, M. Kachanovska, M. Wess
Convergence analysis of time-domain PMLs for 2D electromagnetic wave propagation in dispersive waveguides (2023)
ESAIM: Math. Modell. Numer. Anal. images/icons/doctype_pdf.gif
É. Bécache, M. Kachanovska
Stability and Convergence Analysis of Time-Domain Perfectly Matched Layers for the Wave Equation in Waveguides (2021)
SIAM Journal on Numerical Analysis - vol. 59 (4) (pp 2004-2039 ) images/icons/doctype_pdf.gif
É. Bécache, S. Fliss, M. Kachanovska, M. Kazakova
On a surprising instability result of Perfectly Matched Layers for Maxwell's equations in 3D media with diagonal anisotropy (2021)
Comptes Rendus. Mathématique - vol. 3 (pp 249-256 ) 
É. Bécache, P. Joly, V. Vinoles
On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials (2018)
Mathematics of Computations - vol. 87 (pp 2775--2810 ) images/icons/doctype_link.gif
É. Bécache, M. Kachanovska
Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: Necessary and sufficient conditions of stability (2017)
ESAIM: Mathematical Modelling and Numerical Analysis (M2AN) - vol. 51, number 6 (pp 2399 - 2434 ) images/icons/doctype_pdf.gifimages/icons/doctype_pdf.gifimages/icons/doctype_pdf.gif
É. Bécache, P. Joly, M. Kachanovska
Stable Perfectly Matched Layers for a Cold Plasma in a Strong Background Magnetic Field (2017)
Journal of Computational Physics - vol. 341 (pp 76-101 ) 
É. Bécache, L. Bourgeois, J. Dardé, L. Franceschini
Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case (2015)
Inverse Problems and Imaging - vol. 9/4 (pp 971-1002 ) images/icons/doctype_pdf.gif
É. Bécache, P. Joly, M. Kachanovska, V. Vinoles
Perfectly matched layers in negative index metamaterials and plasmas (2015)
ESAIM: Proceedings and Surveys - EDP Sciences - vol. 50 (pp 113-132 ) 
T. Hagstrom, É. Bécache, D. Givoli, K. Stein
Complete Radiation Boundary Conditions for Convective Waves (2012)
Communications in Computational Physics - vol. 11(2) (pp 610-628 ) 
É. Bécache, A. Prieto
Remarks on the stability of Cartesian PMLs in corners (2012)
APNUM - vol. 62 (pp 1639-–1653 ) images/icons/doctype_link.gif
D. Rabinovich, D. Givoli, É. Bécache
Comparison of High-Order Absorbing Boundary Conditions and Perfectly Matched Layers in the Frequency Domain (2010)
International Journal for Numerical Methods in Biomedical Engineering - vol. 26 (pp 1351-1369 ) 
É. Bécache, D. Givoli, T. Hagstrom
High Order Absorbing Boundary Conditions for Anisotropic and Convective Wave Equations (2010)
JCP - vol. 229 (4) (pp 1099-1129 ) 
É. Bécache, J. Rodríguez, C. Tsogka
Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition (2009)
Mathematical Modelling and Numerical Analysis - vol. 43 (2) (pp 377--398 ) images/icons/doctype_link.gif
É. Bécache, J. Rodríguez, C. Tsogka
The Fictitious domain method and applications in wave propagation. Part A and B: The acoustic and the elastic case. (2009)
ECCOMAS Thematic Conference images/icons/doctype_link.gif
É. Bécache, J. Rodríguez, C. Tsogka
A fictitious domain method with mixed finite elements for elastodynamics (2007)
SIAM J. Sci. Comput. - vol. 29 (3) (pp 1244--1267 ) images/icons/doctype_link.gif
É. Bécache, A.-S. Bonnet-BenDhia, G. Legendre
Perfectly matched layers for time-harmonic acoustics in the presence of a uniform flow (2006)
SIAM Journal on Numerical Analysis - vol. 44 (3) (pp 1191-1217 ) images/icons/doctype_link.gif
É. Bécache, P. Joly, J. Rodríguez
Space-time mesh refinement for elastodynamics. Numerical results (2005)
Comput. Methods Appl. Mech. Engrg. - vol. 194 (pp 355-366 ) images/icons/doctype_link.gif
É. Bécache, A. Chaigne, G. Derveaux, P. Joly
Numerical simulation of a guitar (2005)
Computers and structures - vol. 83 (2-3) (pp 107-126 ) 
É. Bécache, G. Derveaux, P. Joly
An efficient numerical method for the resolution of the Kirchhoff-Love dynamic plate equation (2005)
Numerical Methods for Partial Differential Equations - vol. 21 (2) (pp 323 - 348 ) images/icons/doctype_link.gif
É. Bécache, A. Kiselev
Non-stationary elastic wavefields from an apodized normal transducer. Near-field asymptotics and numerics (2005)
Acta Acustica united with Acustica - vol. 91 (5) (pp 822-830 ) 
É. Bécache, P. Joly, J. Rodriguez
A DUAL-PRIMAL COUPLING TECHNIQUE WITH LOCAL TIME STEP FOR WAVE PROPAGATION PROBLEMS (2005)
ECCOMAS Thematic Conference images/icons/doctype_link.gif
É. Bécache, A.-S. Bonnet-BenDhia, G. Legendre
Perfectly matched layers for the convected Helmholtz equation (2004)
SIAM Journal on Numerical Analysis - vol. 42 (pp 409-433 ) images/icons/doctype_pdf.gif
É. Bécache, A. Ezziani, P. Joly
A mixed finite element approach for viscoelastic wave propagation. (2004)
Computational Geosciences - vol. 8(3) (pp 255-299 ) 
É. Bécache, P. Petropoulos, S. Gedney
On the long-time behavior of unsplit Perfectly Matched Layers (2004)
IEEE Transactions on Antennas and Propagation - vol. 52 (5) 
É. Bécache, S. Fauqueux, P. Joly
Stability of perfectly matched layers, group velocities and anisotropic waves. (2003)
Journal of Computational Physics - vol. 188(2) (pp 399-433 ) 
É. Bécache, A. Chaigne, G. Derveaux, P. Joly
Time-domain simulation of a guitar : Model and method (2003)
Acoustical Society of America Journal - vol. 114(6) (pp 3368 - 3383 ) 
É. Bécache, P. Joly
On the analysis of Bérenger's perfectly matched layers for Maxwell's equations (2002)
ESAIM: Mathematical Modelling and Numerical Analysis - vol. 36(1) (pp 87-119 ) 
É. Bécache, P. Joly, C. Tsogka
A new family of mixed finite elements for the linear elastodynamic problem (2002)
SIAM Journal on Numerical Analysis - vol. 39(6) (pp 2109-2132 ) 
É. Bécache, P. Joly, C. Tsogka
Fictitious domains, mixed finite elements and perfectly matched layers for 2-D elastic wave propagation. (2001)
J. Comput. Acoust. - vol. 9, no. 3 (pp 1175--1201 ) images/icons/doctype_link.gif

Livre

É. Bécache, P. Ciarlet, C. Hazard, E. Lunéville
La méthode des éléments finis : de la théorie à la pratique. Tome 2 : Compléments (2020)
 
É. Bécache, P. Ciarlet, C. Hazard, E. Lunéville
La Méthode des Eléments Finis. De la Théorie à la Pratique. II. Compléments (2010)
Coll. Les Cours, Les Presses de l'ENSTA, 288 pages 

Conférences internationales avec actes

É. Bécache, M. Kachanovska, M. Wess
Stability and convergence of time-domain perfectly matched layers in dispersive waveguides (2022)
(pp 192 ) images/icons/doctype_pdf.gif
É. Bécache, A.-S. Bonnet-BenDhia, S. Fliss, A. Tonnoir
The Half-space Matching method and the Perfectly Matched Layers for scattering problem in anisotropic elastic media (2022)
(pp 402 ) images/icons/doctype_pdf.gif
É. Bécache, M. Kachanovska
Stable Perfectly Matched Layers for a Class of Anisotropic Dispersive Models (2017)
Oberwolfach Report 
É. Bécache, P. Joly, M. Kachanovska
Stable Perfectly Matched Layers for a Simplified Anisotropic Model of Cold Plasma (2015)
(pp 158-159 ) 
É. Bécache, P. Joly, V. Vinoles
Perfectly Matched Layers for dispersive Maxwell’s equations (2015)
 
É. Bécache, P. Joly, J. Rodríguez
A Lagrange multiplier free space-time mesh refinement method for wave propagation problems (2005)
 
É. Bécache, A.-S. Bonnet-BenDhia, G. Legendre
Perfectly Matched Layers for time-harmonic acoustics in the presence of a uniform flow (2005)
 
É. Bécache, A. Ezziani, P. Joly
Mathematical and numerical modeling of wave propagation in viscoelastic media (2003)
Springer (pp 39-48 ) 
É. Bécache, A.-S. Bonnet-BenDhia, G. Legendre
Perfectly matched layers for the convected Helmholtz equation (2003)
SIAM Journal on Numerical Analysis - Springer - vol. 42 (1) (pp 409-433 ) 
É. Bécache, A.-S. Bonnet-BenDhia
PMLs for the numerical simulation of harmonic diffracted waves in an elastic plate (2003)
 
É. Bécache, P. Joly, G. Scarella
A fictitious domain method for a unilateral contact problem (2003)
Springer (pp 431-436 ) 
É. Bécache, A. Kiselev
Detailed study of non-stationary elastic wavefields produced by an apodized normal transducer. Comparisons between asymptotics and numerical results (2003)
(pp 1027-1030 ) 
É. Bécache, S. Gedney, P. Petropoulos
Long-Time Behavior of the Unsplit PML (2003)
Springer-Verlag (pp 120-124, ) 
É. Bécache, A.-S. Bonnet-BenDhia
PMLs for the numerical simulation of harmonic diffracted waves in an elastic plate (2003)
(pp 1019-1022 ) 
É. Bécache, P. Joly, J. Rodríguez
Space-Time Mesh Refinement for the Elastodynamic Equations. (2003)
- Springer (pp 313-318 ) 
É. Bécache, A. Ezziani, P. Joly
Modeling of wave propagation in linear viscoelastic media (2002)
Mathematical modeling of wave phenomena - Mathematical modeling in physics, engineering and cognitive sciences, Vaxjo University Press (pp 39-48 ) 
É. Bécache, P. Joly, J. Rodriguez
Space-time mesh refinement for elastodynamic equations (2002)
 
É. Bécache, A. Chaigne, G. Derveaux, P. Joly
Numerical simulation of a guitar (2001)
 
É. Bécache, P. Joly, G. Scarella
A fictitious domain method for unilateral contact problems in non-destructive testing (2001)
 
É. Bécache, G. Derveaux, P. Joly
An explicit finite element scheme for time-dependent Kirchhoff-Love equations (2000)
Mathematical and numerical aspects of wave propagation (Santiago de Compostela) - SIAM, Philadelphia, PA (pp 735--740 ) 

Conférences sans actes

É. Bécache
Promenade mathématique (2018)
Journée Filles et Maths: une équation lumineuse 
É. Bécache
Promenade mathématique (2018)
Remise des prix des Olympiades Nationales de Mathématiques 
É. Bécache
Voir et comprendre en mathématiques (2017)
Festival d'Astronomie de Fleurance du 5 au 11 aout 2017 (conférence grand public) images/icons/doctype_link.gif
É. Bécache
Comment modéliser et simuler numériquement la propagation de la lumière, du son ou plus généralement des ondes dans les étoiles et planètes ? (2017)
Festival d'Astronomie de Fleurance du 5 au 11 aout 2017 (Fil noir) 
É. Bécache
Stable Perfectly Matched Layers for a Class of Anisotropic Dispersive Media (2017)
NUMELEC 2017 
É. Bécache, L. Bourgeois, J. Dardé, L. Franceschini
The method of quasi-reversibility for time-dependent wave equation. Application to the inverse obstacle problem (2015)
Inverse Problems in Wave Propagation, Bremen, Allemagne, 7-10/4/2015 
É. Bécache
Some contributions to Perfectly Matched Layers (2008)
WCCM8 / ECCOMAS 2008, June 30 --July 5, 2008, Venice, Italy 
É. Bécache, P. Joly, J. Rodríguez
Présentation et analyse des méthodes de raffinement de maillage espace-temps conservatives pour des problèmes de propagation d'ondes (2007)
8eme Colloque en Calcul des Structures. Giens, France 
É. Bécache, P. Joly, J. Rodríguez
Analysis of a space-time mesh refinement method for wave propagation problems (2005)
The Sixth European Conference on Numerical Mathematics and Advanced Applications (ENUMATH'05). Universidad de Santiago de Compostela, Spain 
É. Bécache, P. Joly, J. Rodriguez
A DUAL-PRIMAL COUPLING TECHNIQUE WITH LOCAL TIME STEP FOR WAVE PROPAGATION PROBLEMS (2005)
ECCOMAS/ COUPLED PROBLEMS 2005 
É. Bécache, A.-S. Bonnet-BenDhia, G. Legendre
Perfectly Matched Layers for the solution of time harmonic diffraction problems in waveguides. (2004)
PIERS (Progress In Electromagnetic Research Symposium), Pise 
É. Bécache, A.-S. Bonnet-BenDhia, G. Legendre
Perfectly Matched Layers for time-harmonic aero-acoustics. (2004)
6th International Conference on Spectral and High-Order Methods (ICOSAHOM'04) 
É. Bécache, P. Joly, J. Rodríguez
Raffinement de maillage local spatio-temporel pour les équations de l'élastodynamique (2003)
35éme Congrés National d'Analyse Numérique. La Grande Motte, France 
É. Bécache, A. Ezziani, P. Joly
Modeling of wave propagation in linear viscoelastic media (2003)
Mathematical modelling in physics, engineering and cognitive sciences 
É. Bécache, P. Joly, A. Ezziani
Propagation d'ondes dans les milieux viscoélastiques linéaires (2003)
Conférence du GDR 2501, Aussois 

H.D.R.

É. Bécache
Méthodes variationnelles, domaines fictifs et conditions aux limites artificielles pour des problèmes hyperboliques linéaires. Applications aux ondes dans les solides (2003)
- Habilitation Université Paris-Dauphine images/icons/doctype_pdf.gifimages/icons/doctype_link.gif

Rapports de recherche

É. Bécache, A. Prieto
Remarks on the stability of Cartesian PMLs in corners (2011)
 images/icons/doctype_link.gifimages/icons/doctype_link.gif
É. Bécache, J. Rodríguez, C. Tsogka
On the convergence of the fictitious domain method for wave propagation problems (2006)
 images/icons/doctype_link.gif
É. Bécache, A. Ezziani, P. Joly
Modélisation de la propagation d'ondes dans les milieux viscoélastiques linéaires II : Analyse numérique (2004)
 images/icons/doctype_link.gif
É. Bécache, A. Ezziani, P. Joly
Modélisation de la propagation d'ondes dans les milieux viscoélastiques linéaires : I. Analyse mathématique (2003)
 images/icons/doctype_link.gif
É. Bécache, A. Ezziani, P. Joly
Modélisation mathématique et numérique des ondes dans les milieux viscoélastiques monodimensionnels (2001)
 
É. Bécache, P. Joly, C. Tsogka
Recent Developments in Mixed Finite Elements for Elastodynamics in Complex Media (1999)
 

Prépublication

É. Bécache, A.-S. Bonnet-Ben Dhia, S. Fliss, A. Tonnoir
The Half-Space Matching method for elastodynamic scattering problems in unbounded domains (2022)
 

Cours

É. Bécache
Analyse numérique des équations d'ondes en régime transitoire. (2009)
 
É. Bécache, P. Joly, C. Tsogka
Méthodes numériques : Éléments finis mixtes et méthode des domaines fictifs pour l'élastodynamique (2001)
Ecole des Ondes : Ondes élastiques dans les solides images/icons/doctype_pdf.gifimages/icons/doctype_link.gif
É. Bécache
L’approximation filaire en régime harmonique (1999)
 images/icons/doctype_pdf.gif