Selected Publications

This article deals with boundary integral equation preconditioning for the multiple scattering problem. The focus is put on the single scattering preconditioner, corresponding to the diagonal part of the integral operator, for which two results are proved. Indeed, after applying this geometric preconditioner, it appears that, firstly, every direct integral equations become identical to each other, and secondly, that the indirect integral equation of Brakhage–Werner becomes equal to the direct integral equations, up to a change of basis. These properties imply in particular that the convergence rate of a Krylov subspaces solver will be exactly the same for every preconditioned integral equations. To illustrate this, some numerical simulations are provided at the end of the paper.
Journal of Mathematical Analysis and Applications, 2014

A time harmonic far field model for closed electromagnetic time reversal mirrors is proposed. Then, a limit model corresponding to small perfectly conducting scatterers is derived. This asymptotic model is used to prove the selective focusing properties of the time reversal operator. In particular, a mathematical justification of the decomposition of the time reversal operator (DORT) method is given for axially symmetric scatterers.
SIAM J. Appl. Math., 2008

Recent Publications

More Publications

. Integral equation based optimized Schwarz method for electromagnetics. Accepted for publication in the proceedings of the DDXXIV International Conference, 2018.

. GetDDM: an Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic Wave Problems. Computer Physics Communications, 2016.

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. A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations. Journal of Computational Physics, 2015.

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Projects

Mu-diff

Matlab toolbox to solve two dimensional acoustic multiple scattering by disks.

GetDDM

GetDDM is an open-source framework for testing Schwarz-type domain decomposition methods for time-harmonic wave problems.

Infomath

Séminaire des outils informatiques à l’usage des mathématiciennes et mathématiciens

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