Guillaume Legendre

Assistant professor
Université de Paris-Dauphine
Centre de Recherche en Mathématiques de la Décision,
UMR CNRS 7534,
Université de Paris-Dauphine,
PSL Research University,
Place du Maréchal De Lattre De Tassigny,
75775 Paris cedex 16 - France

room: B514bis
tel.: +33 (0)1 44 05 47 26
email: guillaume.legendre

drapeau français Cette page en français.
Research Publications Curriculum vitæ Scientific computing
 I am assistant professor at the CEREMADE of the Paris-Dauphine university.
Research interests in a few keywords: modeling, aeroacoustics, electromagnetism, fluid-structure interaction, ab initio relativistic quantum chemistry, 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 time-harmonic 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.-P. Bérenger, in the time-harmonic domain (work in collaboration with Éliane Bécache).

More recently, I worked with Patrick Ciarlet, Serge Nicaise and Thierry Horsin 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, combined with the method of characteristics, 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.

I also work, notably with Mathieu Lewin and Éric Séré, on the development of mathematically sound computational methods in relativistic quantum chemistry, which takes into account the fine effects encountered by the core electrons in heavy atoms. I am more particularly interested in the implementation and study of the behavior (convergence, discretization issues...) of new algorithms based on previous works from members of the project ACCQUAREL, for models of the Dirac-Hartree-Fock type. These models lead to difficult issues due to the lack of lower bound on the (continuous) spectrum of the Dirac operator. In particular, the considered energies are not bounded from below, a property which forbids to use the usual methods devoted to the non-relativistic case.

 Publications and preprints
A copy of these papers can be requested directly to me by email.

My Ph.D. thesis: Rayonnement acoustique dans un fluide en écoulement : analyse mathématique et numérique de l'équation de Galbrun, (in french, 172 pages, 4.81 Mb), defended on september 29, 2003.
 Curriculum vitæ
 A short version of my curriculum vitæ is available here (Adobe Acrobat Reader required).

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