Publications

        Journaux

1.  Regularization in 3D for anisotropic elastodynamic crack and obstacle problems (with J. C. Nedelec, N. Nishimura), J. of Elasticity, 31, 25-46, 1993.
2. A Variational Boundary Integral Equation Method for an Elastodynamic Antiplane Crack, Int. J. for Numerical Meth. in Eng., vol 36,  no. 6, 969--984, 1993.
3. A Space-Time Variational Formulation for the Boundary Integral Equation in a 2D Elastic Crack Problem (with T. Ha Duong), RAIRO M2AN, vol 28,  no. 2, 141--176, 1994.
4. Construction and analysis of a new mixed finite element allowing mass lumping. (with Chrysoula Tsogka and Patrick Joly), C.R. Acad. Sci. Paris, Analyse numérique, t. 324, Série I, 1997.
5.  Mixed finite elements and mass lumping for linear elastodynamics. (I) Construction. (with Chrysoula Tsogka and Patrick Joly), C.R. Acad. Sci. Paris, Analyse numérique, t. 325, Série I, 1997.
6.  Higher-order variational finite difference schemes for solving 3-D paraxial wave equations using splitting techniques (with F. Collino and P. Joly),  Wave Motion 31 (2000), no. 2, 101--116.
   
7.  An analysis of new mixed finite elements for the approximation of wave propagation problems (with Chrysoula Tsogka and Patrick Joly), SINUM , Vol. 37 Number 4 pp. 1053-1084 , 2000.
8. Fictitious Domains, Mixed Finite Elements and Perfectly Matched Layers for 2D Elastic Wave Propagation (with Chrysoula Tsogka and Patrick Joly), J. of Comp. Acous. , Vol. 9, No. 3 (September 2001) , 1175--1203.
9. A new family of mixed finite elements for the linear elastodynamic problem, (with Chrysoula Tsogka and Patrick Joly),  SINUM , Vol. 39 Number 6,  2109--2132, 2002.
10. On the analysis of Berenger's Perfectly Matched Layers for Maxwell's equations (with P. Joly), M2AN, vol. 36 No 1, pp 87-120, 2002.
    
11. Stability of Perfectly Matched Layers, Group Velocities and Anisotropic Waves, (with S. Fauqueux and P. Joly), J. Comp. Phys.,  188,  pp 399-433, 2003.
12. Time-domain simulation of a guitar: Model and method, (with A. Chaigne, G. Derveaux and P. Joly), J. Acoust. Soc. Am., 6, 114, 2003, p. 3368 - 3383.
13. Perfectly matched layers for the convected Helmholtz equation, (with A.-S. Bonnet and G. Legendre),  SIAM Journal on Numerical Analysis,Volume 42, Number 1, pp. 409-433, 2004.
14. On the long-time behavior of unsplit Perfectly Matched Layers , (with P. G. Petropoulos and S. Gedney),  IEEE AP-Transactions, vol 52, No 5, May 2004.
15. A mixed finite element approach for viscoelastic wave propagation,  (with A. Ezziani and P. Joly), Comput. Geosci. 8 (2004), no. 3, 255--299.
16. Space-Time Mesh Refinement for   Elastodynamics. Numerical Results, (with P. Joly and J. Rodriguez), Comput. Methods Appl. Mech. Engrg. 194 (2005), no. 2-5, 355--366.
17. Numerical simulation of a guitar, (with A. Chaigne, G. Derveaux and P. Joly), Comput. & Structures 83 (2005), no. 2-3, 107--126.
18. An efficient numerical method for the resolution of the Kirchhoff-Love dynamic plate equation, (with G. Derveaux and P. Joly), Numer. Methods Partial Differential Equations 21 (2005), no. 2, 323--348.
19.   Non-stationary elastic wavefields from an apodized normal transducer. Near-field asymptotics and numerics,  (with  A. Kiselev), Acta Acustica united with Acustica, vol 91, 5, pp 822--830, (2005)
20.   Perfectly matched layers for time-harmonic acoustics in the presence of a uniform flow, (with A.-S. Bonnet and G. Legendre),SINUM, Volume 44, Issue 3, Pages 1191-1217 (2006)
21. Bécache, E.; Rodríguez, J.; Tsogka, C. A fictitious domain method with mixed finite elements for elastodynamics. SIAM J. Sci. Comput. 29 (2007), no. 3, 1244--1267
22. Bécache, E.; Rodríguez, J.; Tsogka, C.Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition. ESAIM: M2AN 43 (2009) 377–398.
    
23. High Order Absorbing Boundary Conditions for Anisotropic and Convective Wave Equations, (with D. Givoli and T. Hagstrom), to appear in JCP.
    

     Preprints

1. Higher-Order Numerical Schemes and Operator Splitting for Solving 3D Paraxial Wave Equations in Heterogeneous Media (with F. Collino and P. Joly), Rapport de recherche, INRIA , 3497, septembre 98.
2. Some New Mixed Finite Elements in View of the Numerical Solution of Time Dependent Wave Propagation Problems, (with Chrysoula Tsogka and Patrick Joly), Rapport de recherche, INRIA , 3445, juin 98.
3. Mixed Finite Elements, Strong Symmetry and Mass Lumping for Elastic Waves, (with Chrysoula Tsogka and Patrick Joly), Rapport de recherche, INRIA ,3717, septembre 98.
4. On the analysis of Berenger's Perfectly Matched Layers for Maxwell's equations (with P. Joly),  Rapport de Recherche INRIA, 4164, avril 2001.
5. Stability of Perfectly Matched Layers, Group Velocities and Anisotropic Waves, (with S. Fauqueux and P. Joly),  Rapport de Recherche INRIA,  4304, 2001.(Erratum dans le RR: Lemma 6: lire condition C2-(i) (et non pas (ii)))
6. On the analysis of Berenger's Perfectly Matched Layers for Maxwell's equations (with P. Joly), Rapport de Recherche INRIA,  4164, 2001.
7. On the long-time behavior of unsplit Perfectly Matched Layers , (with P. G. Petropoulos and S. Gedney),  Rapport de Recherche INRIA,  4538,  2002.
   
8. Perfectly matched layers for the convected Helmholtz equation , (with A.-S. Bonnet and G. Legendre), Rapport de Recherche INRIA,  4690, 2003.
9. Modélisation de la propagation d'ondes dans les milieux viscoélastiques linéaires : I. Analyse mathématique, (with A. Ezziani and P. Joly),  Rapport de Recherche INRIA,  4785, 2003.
10. Modélisation de la propagation d'ondes dans les milieux viscoélastiques linéaires : II. Analyse numérique, (with A. Ezziani and P. Joly),  Rapport de Recherche INRIA,  5159, 2004.
11.  Perfectly matched layers for time-harmonic acoustics in the presence of a uniform flow, (with A.-S. Bonnet and G. Legendre), Rapport de Recherche INRIA,  5486, 2005.
12. On the convergence of the fictitious domain method for wave equation problems (with J. Rodriguez and Chrysoula Tsogka), Rapport de Recherche INRIA 37, 2006.

     Articles de conferences internationales

1.  Variational Integral Method in the  Time Domain for Elastic Scattering Problems,  International Boundary Element Symposium, Nice, Mai 1990.
   
2. Reflection tomography : How to cope with multiple   arrivals ?,  (with E. Chovet, F. Delprat-Jannaud, P. Lailly),  62th  S.E.G. Meeting, New-Orleans, Nov. 1992, pp 742-744.
   
3.  On two Migration Methods based on Paraxial Equations  in a 3D heterogeneous Medium., (with F. Collino , M. Kern and P. Joly), Mathematical Methods in Geophysical Imaging III, part of  SPIE's 1995 International Symposium on Optical Science, Engineering and Instrumentation, San Diego, California, July 1995.
4. Higher order numerical schemes for paraxial approximations of the wave equation , (with F. Collino,   P. Joly),  2nd International Conference on Theoretical and  Computational Acoustics, August 1995.
5. 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, (with P. Joly, C. Tsogka),  Fourth Int. Conf. on  Mathematical and numerical aspects of wave propagation (Golden, CO, 1998), 322--326, SIAM, Philadelphia, PA, 1998.
6. An explicit finite element scheme for the time-dependent Kirchhoff-Love equations.(with G. Derveaux and P. Joly),   Fifth Int. Conf. on Mathematical and  numerical aspects of wave propagation (Santiago  de Compostela,  Spain, 2000), 735--740,  SIAM, Philadelphia, 2000 .
7. Numerical simulation of a guitar, (with   A. Chaigne, G. Derveaux and P. Joly),  European  Conf. on Comput. Mech. , Cracow, Poland, 2001.
8. A fictitious domain method for  unilateral contact problems in non-destructive testing . (with P. Joly and  G. Scarella), 1st MIT Conference, June 12-14, 2001, Cambridge, USA.
9. Space-time mesh refinement for elastodynamic equations,    (with  P. Joly and J. Rodriguez), 14th International Conference on Domain Decomposition Methods , January 6-11, 2002 , Mexico.
10. Perfectly matched layers for the convected Helmholtz equation., (with    A.-S. Bonnet, G. Legendre),  Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyvaskyla (Finland), June 30th- July  4th 2003, Springer, pp 142-147.
    
11. A fictitious domain method for  unilateral contact problems in non-destructive testing . (with P. Joly and  G. Scarella), Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyvaskyla (Finland), June  30th- July  4th 2003, Springer, pp 431-436.
    
12. Space-Time Mesh Refinement for the Elastodynamic Equations. (with  P. Joly and J. Rodriguez),  Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyvaskyla (Finland), June  30th- July  4th 2003, Springer, pp 313-318.
    
13. Mathematical and numerical modeling of wave propagation in linear viscoelastic media. (with A. Ezziani and P. Joly), Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyvaskyla (Finland), June  30th- July  4th 2003, Springer, pp 916-921.
    
14. Long-Time Behavior of the Unsplit PML, (with P. G. Petropoulos and S. Gedney), Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyvaskyla (Finland), June  30th- July  4th 2003, Springer, pp 120-124.
    
15. PMLs for the numerical simulation of harmonic diffracted waves in an elastic plate, (with A.-S. Bonnet),World Congress on Ultrasonics 2003, Paris, pp. 1019-1022.
16. Detailed study of non-stationary elastic wavefields produced by an apodized normal transducer. Comparisons between asymptotics and numerical results, (with A. Kiselev), World Congress on Ultrasonics 2003, Paris, pp. 1027-1030.

Quelques notes de cours

• [SC4] Analyse mathématique et numérique de l'équation des ondes , Poly du cours de l'ENSTA.
• [SC1] Equations intégrales pour l'équation des ondes, support de cours de l'école des ondes, INRIA, Janvier 1994.
•  Quelques notes sur la méthode des domaines fictifs pour les ondes
• Approximation filaire en regime harmonique,  École des Ondes INRIA, Diffraction par des
  structures complexes, 1999,  pp 289--316 (slides).
•  Au sujet des PML pour les ondes elastiques

  

Habilitation :