Bertrand Thierry

French National Centre for Scientific Research | CNRS · Laboratoire Jacques-Louis Lions

The optimized Schwarz method (OSM) is recognized as one of the most efficient domain decomposition strategies without overlap for the solution to wave propagation problems in harmonic regime.

We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain decomposition techniques for time-harmonic wave problems. After a review of Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along w...

This paper presents a new non-overlapping domain decomposition method for the time harmonic Maxwell's equations, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Magnetic-to-Electric operator. A convergence theore...

The aim of this paper is to describe a Matlab toolbox, called µ-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in µ-diff are based on the Fourier series expansions of the four basic integral operators arising in scattering theory. Based on...

The aim of this paper is to describe a Matlab toolbox, called μ-diff, which is designed for spectrally solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The formulation is based on the Fourier series expansions of the four basic integral operators arising in scattering problems. Based on these expressi...

This document presents the µ-diff Matlab toolbox that can be used for solving multiple scattering problems by integral equations. The obstacles must be circular cylinders.

We present a flexible finite element solver for testing optimized Schwarz domain decomposition techniques for the time-harmonic Maxwell equations. After a review of nonoverlapping Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver,...

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...

The aim of this paper is to develop an analysis of the distribution of the eigenvalues of the acoustic single-layer potential for various low frequency two-dimensional multiple scattering problems. The obstacles are supposed to be distant (dilute media). In [B. Thierry, Analyse et simulations numériques du retournement temporel et de la diffraction...

The aim of this paper is to derive spectral and condition number estimates of the single-layer operator for low-frequency multiple scattering problems. This work extends to dense media the analysis initiated in Antoine and Thierry (in press) [19]. Estimates are obtained first in the case of circular cylinders by Fourier analysis and are next formal...

Efficient, robust and accurate algorithms are proposed for solving the multiple scattering problem by M circular obstacles for the whole spectrum of frequency. The representation of the solution is based on an integral equation formulation next solved by using Fourier basis. Numerical examples are provided to show that the approaches are efficient.

Cette thèse comporte deux parties. La première est consacrée à l'étude de quelques problèmes inverses de détection et de localisation d'obstacles ou de sources à l'aide d'un miroir à retournement temporel (MRT), appareil pouvant rétro-propager des ondes sur la source qui les a émises. Nous commençons par la méthode DORT qui permet de focaliser séle...

Dans cet exposé, nous présenterons une nouvelle méthode de résolution du problème de diffraction multiple par des cylindres circulaires, en particulier dans le cas où la longueur d'ondes est petite devant la taille caractéristique des cylindres. En effet, il est bien connu que ce régime induit d'importantes difficultés numériques, notamment parce q...

This aim of this talk is to propose a new numerical method for solving the multiple scattering problem of an acoustic wave by circular cylinders. The situation where the wavelength is small compared to the characteristic size of the cylinders is analyzed in detail here. It is known that this framework implies specific numerical difficulties since i...

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...