Marc Bakry
POSTDOCTORAL FELLOW IN APPLIED MATHEMATICS
Photo personnelle

E-mail: marc[DOT]bakry[AT]gmail[DOT]com
Tel.: +33628334784

Research Publications Software PhD thesis About me

Research 


I am currently a post-doc with Matthieu Aussal at the Centre de Mathématiques Appliquées de l'Ecole polytechnique (CMAP) in Palaiseau, France. I work on different subjects among which
  • coupled elasticity-acoustics FEM-BEM formulations with applications in fluid-structure interaction and music instrument design
  • fast compressed method for the numerical computation of convolution products. The Fast Free Memory method (FFM), proposed by Matthieu Aussal, enables the computation of full matrix-vector products with dozen of millions of unknowns on small laboratory-sized servers up to one billion for the Laplace Green kernel.
I also contribute to the Gypsilab framework (see here and here).

Previously, I designed algorithms for the computation of the size-distribution in dense nanoparticles samples using X-ray scattering measurements. This work was supervised by Houssem Haddar and the company Xenocs. When the sample is diluted in some buffer, they do not interact one with the other. The inverse problem is linear and may be solved really efficiently using an Expectation Maximization algorithm. When dealing with a dispersion of nanoparticles or a powder, the nanoparticles do interact one with the other. Physical models yield some interaction models which may be linear (but very restrictive, see the corresponding paper here) but mostly non-linear. In that case, the inverse problem extends to a not-so-nice non-linear and non-convex optimization problem.

For the topics on which I worked during my PhD thesis, see the corresponding section.

Peer-reviewed articles & proceedings: 

  • M.Bakry, O. Bunau and H. Haddar, A robust Expectation-Maximization method for the interpretation of small angle scattering data on dense nanoparticle samples, (accepted, to-be-published in) Journal of Applied Crystallography

  • M. Bakry, S. Pernet et F. Collino, A new accurate residual-based a posteriori error indicator for the BEM in 2D-acoustics,
    Comput. Anal. Appl. 73 (12), 2017, pp. 2501-2514 (HAL link)

  • M. Bakry, A goal-oriented a posteriori error estimate for the oscillating single-layer integral equation,
    Appl. Math. Lett. 69, 2017, pp. 133-137

  • M. Bakry et S. Pernet, A posteriori error control for BEM in 2D-acoustics,
    11th World Congress on Computational Mechanics, 2014 (link)

PhD thesis 


During my PhD (2013-2016, at ONERA Toulouse in the former DTIM/M2SN team), I worked on a posteriori error estimates and auto-adaptive mesh refinement for the BEM in acoustics and electromagnetism. In particular, I extended classical indicators of the literature for Laplace Equation to the Helmholtz equation and I interested myself to the convergence of the resulting autoadaptive refinement algorithms. I also proposed equivalent indicators for Electric Field Integral Equation. However, my main contribution was the introduction of an asymptotically exact error estimates, expressed as a classical L2-norm, whose value is equal to the Galerkin norm of the error. I also proposed a goal-oriented error indicator for the oscillating Single Layer potential.

The manuscript (in French) and the summary (in English) can be downloaded at

Software 


I developed a few softwares during my PhD. thesis for the computation of BEM problems for 2D/3D acoustics and 3D electromagnetism. These codes are written in Fortran 95 using OpenMP or MPI parallelization. I give a short outlook below:
  • BEM2D solves BEM problems for the Laplace and the Helmholtz equation. The integrals are computed using semianalytic integration. I did not implement a compression method. The source code is available on request without any guarantee.

  • BEM3D does the same thing as BEM2D, but in 3D! The singular integrals are computed using the Sauter & Schwab method. While it was designed for the Helmholtz equation, any weakly singular kernels may be integrated. The source code is available on request without any guarantee.

  • my contribution to the code for 3D electromagnetism is licensed and not available. It consists in the parallel implementation of the error indicators proposed in my thesis.
Recently, I started being a contributor to the Gypsilab project. Gypsilab is an open-source software (GPL3.0) written entirely in Matlab. It enables the natural writing of variational formulations arising in the FEM and BEM. In particular, it features a complete H-matrix algebra which overloads some classical Matlab operations like de LU-decomposition. Gypsilab is available at https://github.com/matthieuaussal/gypsilab/.


About me


Education


2013-2016 PhD student at the ONERA, centre de Toulouse, team M2SN. Adviser: Sébastien Pernet (ONERA). Directors: Marc Lenoir & Patrick Ciarlet (both ENSTA/UMA)
2010-2013 double-diplom program at the Technische Universität Stuttgart (Germany) in the Luft- und Raumfahrttechnik Studiengang (aerospace engineering). Specialization in Structure Mechanics and Aerodynamics.
2008-2013 Engineering student at the Institut Supérieur de l'Aéronautique et de l'Espace, formation SUPAERO (ISAE-SUPAERO), "engineering school" (the french system has its own particularities) specialized in aerospace engineering.

Programming skills


Fortran 95 Good knowledge, practiced intensively during my PhD thesis.
Python Operational, though I do not master all the subtleties.
Matlab Operational.
Julia Basic knowledge, a (great) recent discovery.
C/C++ Basic knowledge, sufficient for the design of small programs.

Personal


Enthusiastic glider pilot since 2003 and flight instructor since 2012, I fly at the Centre de Planeur du Sénonais: http://www.planeur-sens.com. I also play piano.