Publications

2012

• Source point discovery through high frequency asymptotic time reversal
  
  • Benamou Jean-David
  • Collino Francis
  • Marmorat Simon
  Journal of Computational Physics, Elsevier, 2012, 231, pp.4643-4661. (10.1016/j.jcp.2012.03.012)
  DOI : 10.1016/j.jcp.2012.03.012
• Complete Radiation Boundary Conditions for Convective Waves
  
  • Hagstrom Thomas
  • Bécache Eliane
  • Givoli Dan
  • Stein Kurt
  Communications in Computational Physics, Global Science Press, 2012, 11 (2), pp.610-628. Local approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated, analyzed, and tested. The results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in [4]. (10.4208/cicp.231209.060111s)
  DOI : 10.4208/cicp.231209.060111s
• A preconditioned 3-D multi-region fast multipole solver for seismic wave propagation in complex geometries
  
  • Chaillat Stéphanie
  • Semblat Jean-François
  • Bonnet Marc
  Communications in Computational Physics, Global Science Press, 2012, 11, pp.594-609. The analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods. In this article, following up on recent studies devoted to the formulation, implementation and evaluation of 3-D single- and multi-region elastodynamic fast multipole boundary element methods (FM-BEMs), a simple preconditioning strategy is proposed. Its efficiency is demonstrated on both the single- and multi-region versions using benchmark examples (scattering of plane waves by canyons and basins). Finally, the preconditioned FM-BEM is applied to the scattering of plane seismic waves in an actual configuration (alpine basin of Grenoble, France), for which the high velocity contrast is seen to significantly affect the overall efficiency of the multi-region FM-BEM. (10.4208/cicp.231209.030111s)
  DOI : 10.4208/cicp.231209.030111s
• Solving the Homogeneous Isotropic Linear Elastodynamics Equations Using Potentials and Finite Elements. The Case of the Rigid Boundary Condition
  
  • Burel Aliénor
  • Imperiale Sébastien
  • Joly Patrick
  Numerical Analysis and Applications, Springer, 2012, 5 (2), pp.136-143. In this article, elastic wave propagation in a homogeneous isotropic elastic medium with rigid boundary is considered. A method based on the decoupling of pressure and shear waves via the use of scalar potentials is proposed. This method is adapted to a finite elements discretization, which is discussed. A stable, energy preserving numerical scheme is presented, as well as 2D numerical results. (10.1134/S1995423912020061)
  DOI : 10.1134/S1995423912020061
• Operator Factorization for Multiple-Scattering Problems and an Application to Periodic Media
  
  • Coatléven Julien
  • Joly Patrick
  Communications in Computational Physics, Global Science Press, 2012, 11 (2), pp.303-318. This work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.
• An elementary introduction to the construction and the analysis of Perfectly Matched Layers for time domain wave propagation
  
  • Joly Patrick
  SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, Springer, 2012, 57, pp.5-48.
• On the use of sampling methods to identify cracks in acoustic waveguides
  
  • Bourgeois Laurent
  • Lunéville Éric
  Inverse Problems, IOP Publishing, 2012, 28 (10), pp.105011.1-105011.18. We consider the identification of cracks in an acoustic 2D/3D waveguide with the help of sampling methods such as the linear sampling method or the factorization method. A modal version of these sampling methods is used. Our paper emphasizes the fact that if one a priori knows the type of boundary condition which actually applies on the crack, then we shall adapt the formulation of our sampling method to such boundary conditions in order to improve the efficiency of the method. The need for such adaptation is proved theoretically and illustrated numerically with the help of 2D examples. We also show by using our modal formulation that the factorization method is applicable in a waveguide with the same data as the linear sampling method. © 2012 IOP Publishing Ltd. (10.1088/0266-5611/28/10/105011)
  DOI : 10.1088/0266-5611/28/10/105011
• Propagation of guided waves through weak penetrable scatterers
  
  • Maurel Agnes
  • Mercier Jean-François
  Journal of the Acoustical Society of America, Acoustical Society of America, 2012, 131 (3), pp.1874-1889. The scattering of a scalar wave propagating in a waveguide containing weak penetrable scatterers is inspected in the Born approximation. The scatterers are of arbitrary shape and present a contrast both in density and in wavespeed (or bulk modulus), a situation that can be translated in the context of SH waves, water waves, or transverse electric/transverse magnetic polarized electromagnetic waves. For small size inclusions compared to the waveguide height, analytical expressions of the transmission and reflection coefficients are derived, and compared to results of direct numerical simulations. The cases of periodically and randomly distributed inclusions are considered in more detail, and compared with unbounded propagation through inclusions. Comparisons with previous results valid in the low frequency regime are proposed. © 2012 Acoustical Society of America. (10.1121/1.3682037)
  DOI : 10.1121/1.3682037
• T-coercivity for scalar interface problems between dielectrics and metamaterials
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Chesnel Lucas
  • Ciarlet Patrick
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2012, 46, pp.1363-1387. Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R^d, with d=2,3. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or coercive + compact) framework. For that, we build some criteria, based on the geometry of the interface between the dielectric and the metamaterial. The proofs combine simple geometrical arguments with the approach of T-coercivity, introduced by the first and third authors and co-worker. Furthermore, the use of localization techniques allows us to derive well-posedness under conditions that involve the knowledge of the coefficients only near the interface. When the coefficients are piecewise constant, we establish the optimality of the criteria. (10.1051/m2an/2012006)
  DOI : 10.1051/m2an/2012006
• Helmholtz equation in periodic media with a line defect
  
  • Coatléven Julien
  Journal of Computational Physics, Elsevier, 2012, 231 (4), pp.1675-1704. We consider the Helmholtz equation in an unbounded periodic media perturbed by an unbounded defect whose structure is compatible with the periodicity of the underlying media. We exhibit a method coupling Dirichlet-to-Neumann maps with the Lippmann-Schwinger equation approach to solve this problem, where the Floquet-Bloch transform in the direction of the defect plays a central role. We establish full convergence estimates that makes the link between the rate of decay of a function and the good behavior of a quadrature rule to approximate the inverse Floquet-Bloch transform. Finally we exhibit a few numerical results to illustrate the efficiency of the method. © 2011 Elsevier Inc. (10.1016/j.jcp.2011.10.022)
  DOI : 10.1016/j.jcp.2011.10.022
• An adaptive algorithm for cohesive zone model and arbitrary crack propagation
  
  • Chiaruttini Vincent
  • Geoffroy Dominique
  • Riolo Vincent
  • Bonnet Marc
  Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, Hermès / Paris : Lavoisier, 2012, 21, pp.208-218. This paper presents an approach to the numerical simulation of crack propagation with cohesive models for the case of structures subjected to mixed mode loadings. The evolution of the crack path is followed by using an adaptive method: with the help of a macroscopic branching criterion based on the calculation of an energetic integral, the evolving crack path is remeshed as the crack evolves in the simulation. Special attention is paid to the unknown fields transfer approach that is crucial for the success of the computational treatment. This approach has been implemented in the finite element code Z-Set (jointly developed by Onera and Ecole des Mines) and is tested on two examples, one featuring a straight crack path and the other involving a complex crack propagation under critical monotonous loading monotonous. (10.1080/17797179.2012.744544)
  DOI : 10.1080/17797179.2012.744544
• Evaluation of 3-D Singular and Nearly Singular Integrals in Galerkin BEM for Thin Layers
  
  • Lenoir Marc
  • Salles Nicolas
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 36, pp.3057-3078. An explicit method for the evaluation of singular and near-singular integrals arising in three-dimensional Galerkin BEM is presented. It is based on a recursive reduction of the dimension of the integration domain leading to a linear combination of one-dimensional regular integrals, which can be exactly evaluated. This method has appealing properties in terms of reliability, precision, and flexibility. The results we present here are devoted to the case of thin layers for the Helmholtz equation, a situation where the panels are close and parallel, known to be difficult in terms of accuracy. Nevertheless, the method applies as well to two-dimensional BEM, secant planes, or even volume integral equations. A MATLAB implementation of the formulas presented here is available online. (10.1137/120866567)
  DOI : 10.1137/120866567
• The Variational Theory of Complex Rays for three-dimensional Helmholtz problems
  
  • Kovalevsky Louis
  • Ladevèze Pierre
  • Riou Hervé
  • Bonnet Marc
  Journal of Computational Acoustics, World Scientific Publishing, 2012, 20, pp.125021 (25 pages). This article proposes an extension of the Variational Theory of Complex Rays (VTCR) to three-dimensional linear acoustics, The VTCR is a Trefftz-type approach designed for mid-frequency range problems and has been previously investigated for structural dynamics and 2D acoustics. The proposed 3D formulation is based on a discretization of the amplitude portrait using spherical harmonics expansions. This choice of discretization allows to substantially reduce the numerical integration work by taking advantage of well-known analytical properties of the spherical harmonics. It also permits (like with the previous 2D Fourier version) an effective \emph{a priori} selection method for the discretization parameter in each sub-region, and allows to estimate the directivity of the pressure field by means of a natural definition of rescaled amplitude portraits. The accuracy and performance of the proposed formulation are demonstrated on a set of numerical examples that include results on an actual case study from the automotive industry. (10.1142/S0218396X1250021X)
  DOI : 10.1142/S0218396X1250021X
• Uniform controllability of scalar conservation laws in the vanishing viscosity limit
  
  • Léautaud Matthieu
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (3), pp.1661-1699. We deal with viscous perturbations of scalar conservation laws on a bounded interval with a general flux function f and a small dissipation coefficient Ɛ. Acting on this system on both endpoints of the interval, we prove global exact controllability to constant states with nonzero speed. More precisely, we construct boundary controls so that the solution is driven to the targeted constant state, and we moreover require these controls to be uniformly bounded as Ɛ → 0+ in an appropriate space. For general (nonconvex) flux functions this can be done for sufficiently large time, and for convex fluxes f, we have a precise estimate on the minimal time needed to control. © 2012 Society for Industrial and Applied Mathematics. (10.1137/100803043)
  DOI : 10.1137/100803043
• A low frequency model for acoustic propagation in a 2D flow duct: numerical computation
  
  • Joubert Lauris
  • Joly Patrick
  Communications in Computational Physics, Global Science Press, 2012, 11 (2), pp.508-524. In this paper we study a low frequency model for acoustic propagation in a 2D flow duct. For some Mach profile flow, we are able to give a well-posedness theorem. Its proof relies on a quasi-explicit expression of the solution which provides us an efficient numerical method. We give and comment numerical results for particular linear, tangent and quadratic profiles. Finally, we give a numerical validation of our asymptotic model.
• Giens 2011
  
  • Bonnet Marc
  • Cornuault Christian
  • Pagano Stéphane
  , 2012.
• Giens 2011
  
  • Bonnet Marc
  • Cornuault Christian
  • Pagano Stéphane
  , 2012.
• Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics
  
  • Grasso Eva
  • Chaillat Stéphanie
  • Bonnet Marc
  • Semblat Jean-François
  Engineering Analysis with Boundary Elements, Elsevier, 2012, 36, pp.744-758. This article extends previous work by the authors on the single- and multi-domain time-harmonic elastodynamic multi-level fast multipole BEM formulations to the case of weakly dissipative viscoelastic media. The underlying boundary integral equation and fast multipole formulations are formally identical to that of elastodynamics, except that the wavenumbers are complex-valued due to attenuation. Attention is focused on evaluating the multipole decomposition of the viscoelastodynamic fundamental solution. A damping-dependent modification of the selection rule for the multipole truncation parameter, required by the presence of complex wavenumbers, is proposed. It is empirically adjusted so as to maintain a constant accuracy over the damping range of interest in the approximation of the fundamental solution, and validated on numerical tests focusing on the evaluation of the latter. The proposed modification is then assessed on 3D single-region and multi-region visco-elastodynamic examples for which exact solutions are known. Finally, the multi-region formulation is applied to the problem of a wave propagating in a semi-infinite medium with a lossy semi-spherical inclusion (seismic wave in alluvial basin). These examples involve problem sizes of up to about $3\,10^{5}$ boundary unknowns. (10.1016/j.enganabound.2011.11.015)
  DOI : 10.1016/j.enganabound.2011.11.015