UMA Home page for Guillaume Legendre
Research activities
Brief summary: During my Ph.D. thesis, I worked, under the supervision of Anne-Sophie Bonnet-Ben Dhia, on aeroacoustics problems. More precisely, I dealt with the numerical resolution of the so-called Galbrun equation in the harmonic time-domain and using a finite element method. In the context of linear acoustics theory, this vectorial equation, established through a mixed Eulerian-Lagrangian reformulation of the linearized fluid mechanics equations, models the wave propagation in an inhomogeneous moving compressible inviscid fluid in adiabatic evolution and uses the Lagrangian displacement vector as dependent variable.
I was also interested in absorbing boundary conditions in aeroacoustics, notably the application of the Perfectly Matched Layers, introduced by J. Bérenger, in the harmonic time domain (work in collaboration with Éliane Bécache).
More recently, I worked with Patrick Ciarlet, Thierry Horsin and Serge Nicaise on the existence of solutions to Maxwell's equations in a chiral medium, with an application to exact boundary controllability.
During my postdoctoral stay at the Centro de Modelamiento Matemático (UMI 2807 CNRS-Universidad de Chile, Santiago, Chile) and in collaboration with Takéo Takahashi, I studied fluid-structure interaction problems and, more particularly, the convergence of a numerical method based on a finite element discretisation of an Arbitrary Lagrangian Eulerian (ALE) formulation of a viscous fluid/rigid body interaction problem. The major difficulties in such an analysis arise from the coupling between the equations of the fluid and those of the structure and from the free boundary of the domain.
Teaching activities (sorry, only french text)
- Vacataire à l'université d'Évry-Val d'Essonne en 2001 et 2002.
- Attaché temporaire d'enseignement et de recherche à l'université de Versailles Saint-Quentin-en-Yvelines pour l'année universitaire 2003/2004.
- Attaché temporaire d'enseignement et de recherche à l'université Paris-Dauphine pour l'année universitaire 2004/2005.
Publications
Papers in peer-reviewed journals
2014
- On the use of perfectly matched layers in the presence of long or backward guided elastic waves
, and
Wave Motion, vol. 51(2), pp. 266-283, 2014
2011
- An alternative to Dirichlet-to-Neumann maps for waveguides
and
C. R. Acad. Sci. Ser. I, vol. 349, pp. 1005-1009, sep, 2011 [
]
2007
- Time-harmonic acoustic propagation in the presence of a shear flow
, , and
J. Comput. Appl. Math, vol. 204(2), pp. 428-439, 2007 [ ] - Well-posedness of the Drude-Born-Fedorov model for chiral media
and
Math. Models Meth. App. Sci., vol. 17(3), pp. 461-484, 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
2004
- Perfectly matched layers for the convected Helmholtz equation
, and
SIAM Journal on Numerical Analysis, vol. 42, pp. 409-433, 2004 [ ]
2001
- Analyse mathématique de l'équation de Galbrun en écoulement uniforme
, et
Comptes Rendus de l'Académie des Sciences - Série IIB - Mécanique, vol. 329(8), pp. 601-606, aoû 2001
International conferences with proceedings
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
- 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 - Regularization of the Time-Harmonic Galbrun's Equations
, and
Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyväskylä, Finland, Springer, 2003
Conferences without proceedings
2010
- A way to use Perfectly Matched Layers in the presence of backward guided elastic waves
and
ECCOMAS Conference on Computational Mechanics - Solids, Structures and Coupled Problems in Engineering (ECCM-2010), may, 2010 [ ]
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
Doctoral these
2003
- Rayonnement acoustique dans un fluide en écoulement : analyse mathématique et numérique de l'équation de Galbrun
ENSTA Paris, sep 2003 [ ]
Research report
2009
- Time-domain study of the DrudeBornFedorov model for a class of heterogeneous chiral materials
, and
Rapport de Recherche hal-00430196, 2009