UMA Home page for Éliane Bécache
Researcher
Dir. Adj. EDMH
Chargé de Recherche
Dir. Adj. EDMH
Chargé de Recherche
Research Habilitation 2003
EMAIL_TEMPLATE
Research activities (sorry, only french text)
- 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.
Teaching activities (sorry, only french text)
- 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.
Publications
Papers in peer-reviewed journals
2023
- Convergence analysis of time-domain PMLs for 2D electromagnetic wave propagation in dispersive waveguides
, and
ESAIM: Math. Modell. Numer. Anal., jul, 2023
- The Half-Space Matching method for elastodynamic scattering problems in unbounded domains
, , and
Journal of Computational Physics, vol. 490, oct, 2023
2021
- On a surprising instability result of Perfectly Matched Layers for Maxwell's equations in 3D media with diagonal anisotropy
, , and
Comptes Rendus. Mathématique, vol. 3, pp. 249-256, 2021 - Stability and Convergence Analysis of Time-Domain Perfectly Matched Layers for the Wave Equation in Waveguides
and
SIAM Journal on Numerical Analysis, vol. 59 (4), pp. 2004-2039, 2021
2018
- On the analysis of perfectly matched layers for a class of dispersive media and application to negative index metamaterials
, and
Mathematics of Computations, vol. 87, pp. 2775--2810, nov, 2018 
2017
- Stable Perfectly Matched Layers for a Cold Plasma in a Strong Background Magnetic Field
, and
Journal of Computational Physics, vol. 341, pp. 76-101, jul, 2017 - Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: Necessary and sufficient conditions of stability
and
ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), vol. 51, number 6, pp. 2399 - 2434, dec, 2017 [
]
2015
- Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case
, , and
Inverse Problems and Imaging, vol. 9/4, pp. 971-1002, nov, 2015 [ ] - Perfectly matched layers in negative index metamaterials and plasmas
, , and
ESAIM: Proceedings and Surveys, vol. 50, pp. 113-132, EDP Sciences, mar, 2015
2012
- Complete Radiation Boundary Conditions for Convective Waves
, , and
Communications in Computational Physics, vol. 11(2), pp. 610-628, 2012 - Remarks on the stability of Cartesian PMLs in corners
and
APNUM, vol. 62, pp. 1639-1653, nov, 2012
2010
- Comparison of High-Order Absorbing Boundary Conditions and Perfectly Matched Layers in the Frequency Domain
, and
International Journal for Numerical Methods in Biomedical Engineering, vol. 26, pp. 1351-1369, 2010 - High Order Absorbing Boundary Conditions for Anisotropic and Convective Wave Equations
, and
JCP, vol. 229 (4), pp. 1099-1129, feb, 2010
2009
- Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition
, and
Mathematical Modelling and Numerical Analysis, vol. 43 (2), pp. 377--398, 2009 - The Fictitious domain method and applications in wave propagation. Part A and B: The acoustic and the elastic case.
, and
ECCOMAS Thematic Conference, COMPDYN (Computational Methods in Structural Dynamics & Earthquake Engineering), 2009
2007
- A fictitious domain method with mixed finite elements for elastodynamics
, and
SIAM J. Sci. Comput., vol. 29 (3), pp. 1244--1267, may, 2007
2006
- Perfectly matched layers for time-harmonic acoustics in the presence of a uniform flow
, and
SIAM Journal on Numerical Analysis, vol. 44 (3), pp. 1191-1217, 2006
2005
- A DUAL-PRIMAL COUPLING TECHNIQUE WITH LOCAL TIME STEP FOR WAVE PROPAGATION PROBLEMS
, and
ECCOMAS Thematic Conference, COUPLED PROBLEMS, 2005 - An efficient numerical method for the resolution of the Kirchhoff-Love dynamic plate equation
, and
Numerical Methods for Partial Differential Equations, vol. 21 (2), pp. 323 - 348, 2005 - Non-stationary elastic wavefields from an apodized normal transducer. Near-field asymptotics and numerics
and
Acta Acustica united with Acustica, vol. 91 (5), pp. 822-830, 2005 - Numerical simulation of a guitar
, , and
Computers and structures, vol. 83 (2-3), pp. 107-126, 2005 - Space-time mesh refinement for elastodynamics. Numerical results
, and
Comput. Methods Appl. Mech. Engrg., vol. 194, pp. 355-366, feb, 2005
2004
- A mixed finite element approach for viscoelastic wave propagation.
, and
Computational Geosciences, vol. 8(3), pp. 255-299, 2004 - On the long-time behavior of unsplit Perfectly Matched Layers
, and
IEEE Transactions on Antennas and Propagation, vol. 52 (5), 2004 - Perfectly matched layers for the convected Helmholtz equation
, and
SIAM Journal on Numerical Analysis, vol. 42, pp. 409-433, 2004 [ ]
2003
- Stability of perfectly matched layers, group velocities and anisotropic waves.
, and
Journal of Computational Physics, vol. 188(2), pp. 399-433, jul, 2003 - Time-domain simulation of a guitar : Model and method
, , and
Acoustical Society of America Journal, vol. 114(6), pp. 3368 - 3383, dec, 2003
2002
- A new family of mixed finite elements for the linear elastodynamic problem
, and
SIAM Journal on Numerical Analysis, vol. 39(6), pp. 2109-2132, 2002 - On the analysis of Bérenger's perfectly matched layers for Maxwell's equations
and
ESAIM: Mathematical Modelling and Numerical Analysis, vol. 36(1), pp. 87-119, jan, 2002
2001
- Fictitious domains, mixed finite elements and perfectly matched layers for 2-D elastic wave propagation.
, and
J. Comput. Acoust., vol. 9, no. 3, pp. 1175--1201, 2001
2000
- An analysis of new mixed finite elements for the approximation of wave propagation problems.
, and
SIAM J. Numer. Anal., vol. 37, no. 4, pp. 1053--1084, 2000 - Higher-order variational finite difference schemes for solving 3-D paraxial wave equations using splitting techniques.
, and
Wave Motion, vol. 31, no. 2, pp. 101--116, 2000 [ ]
1997
- Éléments finis mixtes et condensation de masse en élastodynamique linéaire. I. Construction.
, et
C. R. Acad. Sci. Paris Sér. I Math., vol. 325, no. 5, pp. 545--550, 1997 - Étude d'un nouvel élément fini mixte permettant la condensation de masse.
, and
C. R. Acad. Sci. Paris Sér. I Math., vol. 324, no. 11, pp. 1281--1286, 1997
1994
- A Space-Time Variational Formulation for the Boundary Integral Equation in a 2D Elastic Crack Problem
and
RAIRO M2AN, vol. 28, 1994 [ ]
1993
- Regularization in 3D for anisotropic elastodynamic crack and obstacle problems.
, and
J. of Elasticity, vol. 31, pp. 25-46, 1993 - a Variational Boundary Integral Equation Method for an
Elastodynamic Antiplane Crack
Int. J. for Numerical Meth. in Eng., vol. 36, 1993
Books
2020
- La méthode des éléments finis : de la théorie à la pratique. Tome 2 : Compléments
, , et
pp. 284, mar 2020
2010
- La Méthode des Eléments Finis. De la Théorie à la Pratique. II. Compléments
, , et
Coll. Les Cours, Les Presses de l'ENSTA, 288 pages, nov 2010
International conferences with proceedings
2022
- Stability and convergence of time-domain perfectly matched layers in dispersive waveguides
, and
pp. 192, 15th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2022 - The Half-space Matching method and the Perfectly Matched Layers for scattering problem in anisotropic elastic media
, , and
pp. 402, 15th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2022
2017
- Stable Perfectly Matched Layers for a Class of Anisotropic Dispersive Models
and
Oberwolfach Report, Space-time Methods for Time-dependent Partial Differential Equations, 2017
2015
- Perfectly Matched Layers for dispersive Maxwell’s equations
, and
WAVES 2015, Karlsruhe, jul, 2015 - Stable Perfectly Matched Layers for a Simplified Anisotropic Model of Cold Plasma
, and
pp. 158-159, WAVES 2015, Karlsruhe, jul, 2015
2005
- A Lagrange multiplier free space-time mesh refinement method for wave propagation problems
, and
7th International Conference on Mathematical and Numerical Aspects of Waves (WAVES'05). Brown University (USA), jun, 2005 - Perfectly Matched Layers for time-harmonic acoustics in the presence of a uniform flow
, and
7th International Conference on Mathematical and Numerical Aspects of Waves (WAVES'05), Providence, jun, 2005
2003
- A fictitious domain method for a unilateral contact problem
, and
Springer, pp. 431-436, Mathematical and Numerical Aspects of Wave Propagation, 2003 - Detailed study of non-stationary elastic wavefields produced by an apodized normal transducer. Comparisons between asymptotics and numerical results
and
pp. 1027-1030, World Congress on Ultrasonics, Paris, 2003 - Long-Time Behavior of the Unsplit PML
, and
Springer-Verlag, pp. 120-124,, Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation. Jyvaskyla, Finland, 2003 - Mathematical and numerical modeling of wave propagation in viscoelastic media
, and
Springer, pp. 39-48, Mathematical and numerical aspects of wave propagation, 2003 - PMLs for the numerical simulation of harmonic diffracted waves in an elastic plate
and
WCU 2003 Proceedings, 2003 - PMLs for the numerical simulation of harmonic diffracted waves in an elastic plate
and
pp. 1019-1022, World Congress on Ultrasonics, Paris, 2003 - Perfectly matched layers for the convected Helmholtz equation
, and
SIAM Journal on Numerical Analysis, vol. 42 (1), pp. 409-433, Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyväskylä, Finland, Springer, 2003 - Space-Time Mesh Refinement for the Elastodynamic Equations.
, and
pp. 313-318, Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Springer, jun, 2003
2002
- Modeling of wave propagation in linear viscoelastic media
, and
Mathematical modeling of wave phenomena, pp. 39-48, Mathematical modeling in physics, engineering and cognitive sciences, Vaxjo University Press, 2002 - Space-time mesh refinement for elastodynamic equations
, and
14th International Conference on Domain Decomposition Methods, January 6-11, 2002 , Mexico, 2002
2001
- A fictitious domain method for unilateral contact problems in non-destructive testing
, and
1st MIT conference, June 12-14, 2001, Cambridge, USA, 2001 - Numerical simulation of a guitar
, , and
ECCM (European Conference on Computational Mechanics), June, 2001, Cracow, Poland, 2001
2000
- An explicit finite element scheme for time-dependent Kirchhoff-Love equations
, and
Mathematical and numerical aspects of wave propagation (Santiago de Compostela), pp. 735--740, SIAM, Philadelphia, PA, 2000
1998
- Fictitious domain method applied to the scattering by a crack of transient elastic waves in anisotropic media: a new family of mixed finite elements leading to explicit schemes
, and
pp. 322-326, Fourth Int. Conf. on Mathematical and numerical aspects of wave propagation (Golden, CO, 1998), SIAM, Philadelphia, PA, 1998, 1998
1995
- Higher order numerical schemes for paraxial approximations of the wave equation
, and
2nd International Conference on Theoretical and Computational Acoustics,, aug, 1995 - On two Migration Methods based on Paraxial Equations in a 3D heterogeneous Medium
, , and
Mathematical Methods in Geophysical Imaging III, part of SPIE’s 1995 International Symposium on Optical Science, Engineering and Instrumentation, San Diego, jul, 1995
1992
- Reflection tomography : How to cope with multiple arrivals ?
, , and
62th S.E.G. Meeting, New-Orleans, nov, 1992
1990
- Variational Integral Method in the Time Domain for Elastic Scattering Problems
International Boundary Element Symposium, Nice, may, 1990
Conferences without proceedings
2018
- Promenade mathématique
Journée Filles et Maths: une équation lumineuse, mar 2018 - Promenade mathématique
Remise des prix des Olympiades Nationales de Mathématiques, mai 2018
2017
- Comment modéliser et simuler numériquement la propagation de la lumière, du son ou plus généralement des ondes dans les étoiles et planètes ?
Festival d'Astronomie de Fleurance du 5 au 11 aout 2017 (Fil noir), aoû 2017 - Stable Perfectly Matched Layers for a Class of Anisotropic Dispersive Media
NUMELEC 2017, nov, 2017 - Voir et comprendre en mathématiques
Festival d'Astronomie de Fleurance du 5 au 11 aout 2017 (conférence grand public), aoû 2017
2015
- The method of quasi-reversibility for time-dependent wave equation. Application to the inverse obstacle problem
, , and
Inverse Problems in Wave Propagation, Bremen, Allemagne, 7-10/4/2015, apr, 2015
2008
- Some contributions to Perfectly Matched Layers
WCCM8 / ECCOMAS 2008, June 30 --July 5, 2008, Venice, Italy, jul, 2008
2007
- Présentation et analyse des méthodes de raffinement de maillage espace-temps conservatives pour des problèmes de propagation d'ondes
, et
8eme Colloque en Calcul des Structures. Giens, France, mai 2007
2005
- A DUAL-PRIMAL COUPLING TECHNIQUE WITH LOCAL TIME STEP FOR WAVE PROPAGATION PROBLEMS
, and
ECCOMAS/ COUPLED PROBLEMS 2005, 2005 - Analysis of a space-time mesh refinement method for wave propagation problems
, and
The Sixth European Conference on Numerical Mathematics and Advanced Applications (ENUMATH'05). Universidad de Santiago de Compostela, Spain, jul, 2005
2004
- Perfectly Matched Layers for the solution of time harmonic diffraction problems in waveguides.
, and
PIERS (Progress In Electromagnetic Research Symposium), Pise, mar, 2004 - Perfectly Matched Layers for time-harmonic aero-acoustics.
, and
6th International Conference on Spectral and High-Order Methods (ICOSAHOM'04), jun, 2004
2003
- Modeling of wave propagation in linear viscoelastic media
, and
Mathematical modelling in physics, engineering and cognitive sciences, 2003 - Propagation d'ondes dans les milieux viscoélastiques linéaires
, and
pp. 11-20, Conférence du GDR 2501, Aussois, Etude de la propagation ultrasonore en milieux non-homogènes en vue du controle non destructif, dec, 2003 - Raffinement de maillage local spatio-temporel pour les équations de l'élastodynamique
, et
35éme Congrés National d'Analyse Numérique. La Grande Motte, France, jun 2003
Habilitation these
2003
- Méthodes variationnelles, domaines fictifs et conditions aux limites artificielles pour des problèmes hyperboliques linéaires. Applications aux ondes dans les solides
Habilitation Université Paris-Dauphine, 2003 [ ]
Doctoral these
1991
- Résolution par une méthode d'équations intégrales d'un problème de diffraction d'ondes élastiques transitoires par une fissure
Thèse de doctorat de l'université Paris 6, Spécialité Mathématiques, sous la direction de Jean-Claude Nédélec, préparée au CMAP (Ecole Polytechnique), 1991
Research reports
2011
- Remarks on the stability of Cartesian PMLs in corners
and
Rapport Recherche INRIA, vol. RR-7620, 2011
2006
- On the convergence of the fictitious domain method for wave propagation problems
, and
Technical Report 5802 INRIA, pp. 37, jan, 2006
2004
- Modélisation de la propagation d'ondes dans les milieux viscoélastiques linéaires II : Analyse numérique
, et
RR-5159, Rapport de Recherche INRIA. 2004, avr 2004
2003
- Modélisation de la propagation d'ondes dans les milieux viscoélastiques linéaires : I. Analyse mathématique
, et
RR-4785, Rapport de Recherche INRIA. 2003, mar 2003
2001
- Modélisation mathématique et numérique des ondes dans les milieux viscoélastiques monodimensionnels
, and
Rapport de contrat IFREMER-INRIA, 2001
1999
- Recent Developments in Mixed Finite Elements for Elastodynamics in Complex Media
, and
Rapport annuel, Consortium SIGMA (Seismic Inversion, Geophysical Modeling and Applications), 1999
1998
- New finite elements for the linear elatodynamics problem
, and
Rapport annuel, Consortium SIGMA (Seismic Inversion, Geophysical Modeling and Applications), 1998
1995
- Higher Order Numerical Schemes for the Paraxial Wave Equation.
, and
Rapport annuel, Consortium PSI (Prestack Structural Interpretation), 1995., 1995
1994
- Some new developments about paraxial approximations for the 3D wave equation.
, and
Rapport annuel, Consortium PSI (Prestack Structural Interpretation), 1994., 1994
1993
- Numerical analysis of adaptive stepize schemes for the approximation of the ray equations
and
Rapport annuel, Consortium PSI (Prestack Structural Interpretation), 1993., 1993
1992
- Reflection tomography: How to cope with multiple arrivals ? Part I: Method and preliminary results.
, , and
3ème rapport annuel, Consortium PSI (Prestack Structural Interpretation), Septembre 1992., 1992 - Reflection tomography: How to cope with multiple arrivals ? Part II : A new gradient computation method: continuous and discrete problems.
3ème rapport annuel, Consortium PSI (Prestack Structural Interpretation), Septembre 1992., 1992
Preprint
2022
- The Half-Space Matching method for elastodynamic scattering problems in unbounded domains
, , and
2022
Lecture notes
2009
2001
- Méthodes numériques : Éléments finis mixtes et méthode des domaines fictifs pour l'élastodynamique
, and
pp. 3--129, Ecole des Ondes : Ondes élastiques dans les solides, nov, 2001 [ ]
1999
- L’approximation filaire en régime harmonique
pp. 289--316, École des Ondes INRIA : "Diffraction par des structures complexes", 1999 [ ]
1995
- Modélisation du problème direct par approximation de Born + rais
École des Ondes INRIA : "Problèmes inverses en propagation d'ondes", 1995 [ ]
1994
- Équations Intégrales pour l'équation des ondes
École des Ondes INRIA : "Méthodes numériques d'ordre élevé pour les ondes en régimes transitoires", 1994 [ ]
Multimedia
2017
- Voir et comprendre en mathématiques
Festival d'Astronomie de Fleurance, aoû 2017