Page of Guillaume Legendre

Teacher / Researcher
Maître de Conférence
PhD defended in 2003

Personal web page

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Research Activities

Research interests in a few keywords: modeling, aeroacoustics, electromagnetism, elastodynamics, fluid-structure interaction, chiral material, Arbitrary Lagrangian Eulerian, perfectly matched layers, controllability, partial differential equations, finite element methods, numerical analysis, scientific computing.
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.

Conferences without proceedings

ECCOMAS Conference on Computational Mechanics - Solids, Structures and Coupled Problems in Engineering (ECCM-2010) images/icons/doctype_pdf.gif
PIERS (Progress In Electromagnetic Research Symposium), Pise 
6th International Conference on Spectral and High-Order Methods (ICOSAHOM'04)