Research Interests

My projects/grants STIC/ANR/ARC/...

My PhD students

Contribution to PhD-defense committees

Helmholtz and Maxwell equations in exterior domain - Forward problem

** Després's Integral Equations
    with A. Bachelot, L. Gatard, K. Mer-Nkonga (Bordeaux)

Resolution of the Després's Integral Equations for high frequencies, using a coupling of Fast Multipole Methods and Microlocal Discretisation, within
           * the Helmholtz equation
           * the Maxwell equations

** OSRC Preconditioning
    with X. Antoine (Nancy), M. Darbas (Amiens), Y. Lafranche (Rennes)

Application of the Fast Multipole Methods to integral equations preconditioned by OSRC techniques and eigenvalues investigation in the case of
           * Helmholtz equation.
           * Maxwell equations.

Membre du projet ANR MicroWave

** Ultra-Weak Variational Formulation and integral representation
    with P. Monk (Delaware)

Coupling of the ultra-weak variational formulation with an integral representation by using
           * a one-level fast multipole method
           * a multilevel fast multipole method

** Coupling finite elements and integral representation
    with N. Gmati (Tunisie), D. Martin (Rennes)

Coupling of the finite elements with an integral representation by using a Schwarz algorithm.
           * Supported by the project STIC-Tunisie 0903
           * with Rania Rais -- PhD student -- AUF (Sept 2009 - Feb 2014): Justification using Schwarz decomposition method, analysis of convergence of Krylov solvers

** Volume and boundary integral equations
    with M. Costabel, E.-H. Koné, H. Sakly, R. Sauleau (Rennes)

Theoretical study of the volume and boundary integral formulations. Numerical resolution of the volume integral equations. Application to the shape optimisation of lens-antennas in collaboration with the IETR.
           * member of the project UEB-EPT OPTIMISE
           * within El-Hadji Koné's PhD (Nov. 2005 - Jun. 2010)

Spectral analysis of the volume integral operators.
           * with Hamdi Sakly -- PhD student (Sept. 2010 - May 2014)

** Integral operators and MELINA++
    with D. Martin (Rennes), E.H. Koné (PhD Rennes), Y. Lafranche (Rennes), R. Rais (PhD Rennes-Tunis), N. Salles (PhD ENSTA),

* Adding surface and volume integral operators to the library MELINA++ (with D. Martin and E.H. Koné).
* Solving Després Integral equations with MELINA++ (with D. Martin).
* Treatment of the singularities using new analytical developments (with N. Salles).
* Adding integral operators and finite-element integrands needed for the exterior Maxwell equations with exact artificial boundary condition (with Y. Lafranche and R. Rais).

The library, maintained by Y. Lafranche and myself, is available on: MELINA++ distribution

** Development of the finite element library XLiFE++
    with C. Chambeyron (ENSTA), M. H. Nguyen (ENSTA), N. Kielbasiewicz (ENSTA), Y. Lafranche (Rennes), M. Lenoir (ENSTA), E. Lunéville (ENSTA), L. Goudenège (Marne-la-Vallée)

See the website: XLiFE++

** FastMMLib: A generic Fast-Multipole-Methods library
    with Y. Lafranche (Rennes)

Helmholtz and Maxwell equations in exterior domain - Inverse problem

** Linear Sampling Method
    with F. Cakoni, D. Colton (Delaware)

Study of the method in the case of screens with
           * an homogeneous boundary condition
           * a mixed boundary condition

Other applications of Fast Multipole Methods

** Molecular dynamics - with IPSO and CERMICS

* A regularized fast multipole method for molecular simulations
* Member of the project ARC HYBRID.
* Member of the project ANR MEGAS.

** Tomography - with R. Potthast (Reading - UK)

Enriched finite elements

** Enriched finite elements for Timoshenko model
    with R. Cornaggia, L. Le Marrec, F. Mahé

Finite elements for cardiac activity

** Simulation of the cardiac electric activity of the left ventricle
    with V. Le Rolle (LTSI)

Modelisation and optimisation in agricultural systems

** Optimisation of Pig Fattening units
    with M. Davoudkhani (PhD INRA), F. Garcia-Launay (INRA), F. Mahé (IRMAR), J.Y. Dourmad (INRA), A. Gohin (INRA)

Different optimisation models
           * optimising feeding and shipping strategy
           * optimising including environmental impact
           * multi-objective optimisation

** Modelisation of cells differentiation
    with I. Louveau (INRA), M.H. Perruchot (INRA), F. Mahé (IRMAR)


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