Publications

2011

• Wave-based crack imaging in elastic solids using 3D time-domain topological sensitivity
  
  • Bellis Cédric
  • Bonnet Marc
  , 2011.
• Dynamical identification of cracks in 3D elastic bodies using topological sensitivity
  
  • Bellis Cédric
  • Bonnet Marc
  , 2011.
• Coupling between a Particle In Cell method and a H 1-conform mixed spectral finite element approximation of Maxwell's equations
  
  • Cohen Gary
  • Sinding Alexandre
  , 2011. This paper describes the coupling between a Particle In Cell (PIC) method and a H 1-conform mixed spectral finite element approximation of Maxwell's equations for the approximation of low dense plasmas. It uses the H 1-conform mixed spectral method already described in [2]. As particle methods themselves are a classical subject, we mainly focus on the coupling between a finite element method on an unstructured grid and a PIC method. This subject has already been studied for a coupling between a PIC method and a discontin-uous Galerkin scheme [4], but its still a challenging subject and the rehabilitation of continuous methods to this aim hasn't been studied yet. The critical point lies in the coupling between an Eulerian approximation of the fields on an unstructured grid and a Lagrangian description of particles motion. This point can heavily penalize the global cost of the algorithm, if not taken into account carefully. In the next sections, a few techniques are introduced and compared to each other in order to obtain an efficient coupling algorithm between these two methods.
• Reconnaissance de motifs dialogiques approchés
  
  • Alès Zacharie
  • Pauchet Alexandre
  , 2011, pp.9-19. Dans le cadre de la modélisation du dialogue, nous présentons une méthode générique permettant l'alignement de motifs approchés en deux dimensions appliquée à des matrices d'annotations codant des dialogues. L'approche utilisée, basée sur un algorithme de programmation dynamique et une mesure de similarité, permet l'identification de motifs similaires à un motif de référence. Ce procédé a été mis en pratique par la recherche de motifs récurrents dans des annotations de dialogues entre parents et enfants, lors de la narration d'histoires enfantines. Les motifs de référence utilisés sont issus d'un précédent travail [12]. Nous présentons brièvement quelques exemples d'alignements obtenus à partir d'un motif.
• Fast and accurate point-based method for time-harmonic maxwell problems involving thin layer materials
  
  • Demaldent Edouard
  • Levadoux David P.
  • Cohen Gary
  Journal of Computational Physics, Elsevier, 2011, 230 (14), pp.5774-5786. We present a high-order hybrid boundary-finite elements method well-suited for solving time-harmonic electromagnetic scattering problems. Actually, this method is specially devoted to perfect electric conductors coated with a thin layer material. On such class of problems this method is shown to be fast and accurate. The fast feature is due to the joint use of finite elements of anisotropic order fitting the layer thickness, and of a point-based boundary element method on the skin. The accuracy is ensured, first by a discretization scheme satisfying the Hcurl-Hdiv conformity required by the integro-differential equation and, secondly, by an adaptive technique of integration based on the detection of some local potential trouble on the geometry such as sharp edges or high dilatation of the elements. This algorithm does not need further information from the user and does not deteriorate the computation time. Numerical examples confirm the efficiency of this approach. © 2011 Elsevier Inc. (10.1016/j.jcp.2011.03.060)
  DOI : 10.1016/j.jcp.2011.03.060
• On simultaneous identification of a scatterer and its generalized impedance boundary condition
  
  • Bourgeois Laurent
  • Chaulet Nicolas
  • Haddar Houssem
  , 2011, pp.28. We consider the inverse scattering problem consisting in the identification of both an obstacle and two functional coefficients of a generalized boundary condition prescribed on its boundary, from far--fields due to several plane waves. After proving a uniqueness result for such inverse problem, we define and compute appropriate derivative of the far--field with respect to an obstacle with non constant impedances. A steepest descent method is then applied to retrieve both the obstacle and the functional impedances from the measured far--fields. The feasability of the method is demonstrated with the help of some 2D numerical experiments.
• On the use of T-coercivity to study the interior transmission eigenvalue problem
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Chesnel Lucas
  • Haddar Houssem
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2011, 349 (11-12), pp.647-651. (10.1016/j.crma.2011.05.008)
  DOI : 10.1016/j.crma.2011.05.008
• Generalized covariation and extended Fukushima decompositions for Banach valued processes. Application to windows of Dirichlet processes.
  
  • Di Girolami Cristina
  • Russo Francesco
  , 2011. This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of Métivier and Pellaumail which is quite restrictive. We make use of the notion of $\chi$-covariation which is a generalized notion of covariation for processes with values in two Banach spaces $B_{1}$ and $B_{2}$. $\chi$ refers to a suitable subspace of the dual of the projective tensor product of $B_{1}$ and $B_{2}$. We investigate some $C^{1}$ type transformations for various classes of stochastic processes admitting a $\chi$-quadratic variation and related properties. If $\X^1$ and $\X^2$ admit a $\chi$-covariation, $F^i: B_i \rightarrow \R$, $i = 1, 2$ are of class $C^1$ with some supplementary assumptions then the covariation of the real processes $F^1(\X^1)$ and $F^2(\X^2)$ exist. \\ A detailed analysis will be devoted to the so-called window processes. Let $X$ be a real continuous process; the $C([-\tau,0])$-valued process $X(\cdot)$ defined by $X_t(y) = X_{t+y}$, where $y \in [-\tau,0]$, is called {\it window} process. Special attention is given to transformations of window processes associated with Dirichlet and weak Dirichlet processes. In fact we aim to generalize the following properties valid for $B=\R$. If $\X=X$ is a real valued Dirichlet process and $F:B \rightarrow \R$ of class $C^{1}(B)$ then $F(\X)$ is still a Dirichlet process. If $\X=X$ is a weak Dirichlet process with finite quadratic variation, and $F: C^{0,1}([0,T]\times B)$ is of class $C^{0,1}$, then $[ F(t, \X_t) ] $ is a weak Dirichlet process. We specify corresponding results when $B=C([-\tau,0])$ and $\X=X(\cdot)$. This will consitute a significant Fukushima decomposition for functionals of windows of (weak) Dirichlet processes. As applications, we give a new technique for representing path-dependent random variables.
• Méthode multipôle rapide multi-niveaux en visco-élastodynamique 3D
  
  • Grasso Eva
  • Chaillat Stéphanie
  • Semblat Jean-François
  • Bonnet Marc
  , 2011, pp.8 p. ; Clé USB. See http://hal.archives-ouvertes.fr/docs/00/59/28/83/ANNEX/r_4VPCS0OY.pdf
• Biologically inspired sensory motor control of a 2-link robotic arm actuated by McKibben muscles
  
  • Jean Frédéric
  • Ouanezar Sofiane
  • Tondu Bertrand
  • Maier Marc
  • Darlot Christian
  • Eskiizmirliler Selim
  , 2011, pp.2785-2791. (10.1109/ICRA.2011.5980553)
  DOI : 10.1109/ICRA.2011.5980553
• Remarks on the stability of Cartesian PMLs in corners
  
  • Bécache Eliane
  • Prieto Andres
  , 2011, pp.18. This work is a contribution to the understanding of the question of stability of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete levels. First, stability results are presented for the Cartesian PMLs associated to a general first-order hyperbolic system. Then, in the context of the pressure-velocity formulation of the acoustic wave propagation, an unsplit PML formulation is discretized with spectral mixed finite elements in space and finite differences in time. It is shown, through the stability analysis of two different schemes, how a bad choice of the time discretization can deteriorate the CFL stability condition. Some numerical results are finally presented to illustrate these stability results.
• On the use of Lamb modes in the linear sampling method for elastic waveguides
  
  • Bourgeois Laurent
  • Le Louër Frédérique
  • Lunéville Éric
  Inverse Problems, IOP Publishing, 2011, 27 (5), pp.055001. (10.1088/0266-5611/27/5/055001)
  DOI : 10.1088/0266-5611/27/5/055001
• Lagrange multipliers in intrinsic elasticity.
  
  • Iosifescu Oana
  • Ciarlet Philippe G.
  • Ciarlet Patrick
  • Sauter Stefan
  • Jun Zou
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2011, 21, pp.651-666. In an intrinsic approach to three-dimensional linearized elasticity, the unknown is the linearized strain tensor field (or equivalently the stress tensor field by means of the constitutive equation), instead of the displacement vector field in the classical approach. We consider here the pure traction problem and the pure displacement problem and we show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations (the form of which depends on the type of boundary conditions considered). Using the Babuška-Brezzi inf-sup condition, we then show that, in each case, the minimizer of the constrained minimization problem found in an intrinsic approach is the first argument of the saddle-point of an ad hoc Lagrangian, so that the second argument of this saddle-point is the Lagrange multiplier associated with the corresponding constraints. Such results have potential applications to the numerical analysis and simulation of the intrinsic approach to three-dimensional linearized elasticity. (10.1142/S0218202511005167)
  DOI : 10.1142/S0218202511005167
• Optimal control under probability constraint
  
  • Carpentier Pierre
  • Chancelier Jean-Philippe
  • Cohen Guy
  , 2011. 1 Problem formulation 2 Modeling improvement 3 Stochastic Arrow-Hurwicz algorithm 4 Numerical results
• Clark-Ocone type formula for non-semimartingales with finite quadratic variation
  
  • Di Girolami Cristina
  • Russo Francesco
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2011, 349 (3-4), pp.209-214. We provide a suitable framework for the concept of finite quadratic variation for processes with values in a separable Banach space $B$ using the language of stochastic calculus via regularizations, introduced in the case $B= \R$ by the second author and P. Vallois. To a real continuous process $X$ we associate the Banach valued process $X(\cdot)$, called {\it window} process, which describes the evolution of $X$ taking into account a memory $\tau>0$. The natural state space for $X(\cdot)$ is the Banach space of continuous functions on $[-\tau,0]$. If $X$ is a real finite quadratic variation process, an appropriated Itô formula is presented, from which we derive a generalized Clark-Ocone formula for non-semimartingales having the same quadratic variation as Brownian motion. The representation is based on solutions of an infinite dimensional PDE. (10.1016/j.crma.2010.11.032)
  DOI : 10.1016/j.crma.2010.11.032
• Numerical MicroLocal Analysis Revisited
  
  • Benamou Jean-David
  • Collino Francis
  • Marmorat Simon
  , 2011, pp.62. The report bundles a theoretical and a numerical papier presenting a stable version of the {\tt NMLA} algorithm as well a a new curvature estimation method and a linearization error correction method.
• A multiscale hp-FEM for 2D photonic crystal bands
  
  • Brandsmeier Holger
  • Schmidt Kersten
  • Schwab Christoph
  Journal of Computational Physics, Elsevier, 2011, 230 (2), pp.349-374. A multiscale generalised hp-finite element method (MSFEM) for time harmonic wave propagation in bands of locally periodic media of large, but finite extent, e.g., photonic crystal (PhC) bands, is presented. The method distinguishes itself by its size robustness, i.e., to achieve a prescribed error its computational effort does not depend on the number of periods. The proposed method shows this property for general incident fields, including plane waves incident at a certain angle to the infinite crystal surface, and at frequencies in and outside of the bandgap of the PhC. The proposed MSFEM is based on a precomputed problem adapted multiscale basis. This basis incorporates a set of complex Bloch modes, the eigenfunctions of the infinite PhC, which are modulated by macroscopic piecewise polynomials on a macroscopic FE mesh. The multiscale basis is shown to be efficient for finite PhC bands of any size, provided that boundary effects are resolved with a simple macroscopic boundary layer mesh. The MSFEM, constructed by combing the multiscale basis inside the crystal with some exterior discretisation, is a special case of the generalised finite element method (g-FEM). For the rapid evaluation of the matrix entries we introduce a size robust algorithm for integrals of quasi-periodic micro functions and polynomial macro functions. Size robustness of the present MSFEM in both, the number of basis functions and the computation time, is verified in extensive numerical experiments. © 2010 Elsevier Inc. (10.1016/j.jcp.2010.09.018)
  DOI : 10.1016/j.jcp.2010.09.018
• Time-domain study of the Drude-Born-Fedorov model for a class of heterogeneous chiral materials
  
  • Ciarlet Patrick
  • Legendre Guillaume
  • Nicaise Serge
  , 2011. We deal with the well-posedness of the transient Maxwell equations in a particular class of heterogeneous chiral material modeled by the Drude-Born-Fedorov constitutive relations. A new formulation of the underlying evolution problem allows us to correct a previous result establishing the existence and uniqueness of the electromagnetic fields in a homogeneous medium.
• Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains
  
  • Abboud Toufic
  • Joly Patrick
  • Rodríguez Jerónimo
  • Terrasse Isabelle
  Journal of Computational Physics, Elsevier, 2011, 230 (15), pp.5877-5907. This work deals with the numerical simulation of wave propagation on unbounded domains with localized heterogeneities. To do so, we propose to combine a discretization based on a discontinuous Galerkin method in space and explicit finite differences in time on the regions containing heterogeneities with the retarded potential method to account the unbounded nature of the computational domain. The coupling formula enforces a discrete energy identity ensuring the stability under the usual CFL condition in the interior. Moreover, the scheme allows to use a smaller time step in the interior domain yielding to quasi-optimal discretization parameters for both methods. The aliasing phenomena introduced by the local time stepping are reduced by a post-processing by averaging in time obtaining a stable and second order consistent (in time) coupling algorithm. We compute the numerical rate of convergence of the method for an academic problem. The numerical results show the feasibility of the whole discretization procedure. © 2011 Elsevier Inc. (10.1016/j.jcp.2011.03.062)
  DOI : 10.1016/j.jcp.2011.03.062
• Accelerated Boundary Element Method for Diffuse Optical Imaging
  
  • Elisee Josias
  • Bonnet Marc
  • Arridge Simon
  Optics Letters, Optical Society of America - OSA Publishing, 2011, 36, pp.4101-4103. The boundary element method (BEM) is a useful tool in Diffuse Optical Imaging (DOI) when modelling large optical regions whose parameters are piecewise constant, but is computationally expensive. We present here an acceleration technique, the single-level Fast Multipole Method, for a highly lossy medium. The enhanced practicability of the BEM in DOI is demonstrated through test examples on single-layer problems, where order of magnitude reduction factors on solution time are achieved, and on a realistic three-layer model of the neonatal head. Our experimental results agree very closely with theoretical predictions of computational complexity. (10.1364/OL.36.004101)
  DOI : 10.1364/OL.36.004101
• Stochastic analysis, random fields and applications VI
  
  • Dalang Robert C.
  • Russo Francesco
  • Dozzi Marco
  , 2011, 63, pp.xi + 492.
• Energy contracts management by stochastic programming techniques
  
  • Cen Zhihao
  • Bonnans J. Frederic
  • Christel Thibault
  Annals of Operations Research, Springer Verlag, 2011, 200 (1), pp.199-222. We consider the problem of optimal management of energy contracts, with bounds on the local (time step) amounts and global (whole period) amounts to be traded, integer constraint on the decision variables and uncertainty on prices only. After building a finite state Markov chain by using vectorial quantization tree method, we rely on the stochastic dual dynamic programming (SDDP) method to solve the continuous relaxation of this stochastic optimization problem. An heuristic for computing sub optimal solutions to the integer optimization problem, based on the Bellman values of the continuous relaxation, is provided. Combining the previous techniques, we are able to deal with high-dimension state variables problems. Numerical tests applied to realistic energy markets problems have been performed. (10.1007/s10479-011-0973-5)
  DOI : 10.1007/s10479-011-0973-5
• Optimal structure of gas transmission trunklines
  
  • Bonnans J. Frederic
  • André Jean
  Optimization and Engineering, Springer Verlag, 2011, 12 (1), pp.175-198. In this paper, we consider the optimal design of a straight pipeline system. Suppose a gas pipeline is to be designed to transport a specified flowrate from the entry point to the gas demand point. Physical and contractual requirements at supply and delivery nodes are known as well as the costs to buy and lay a pipeline or build a compressor station. In order to minimize the overall cost of creation of this mainline, the following design variables need to be determined: the number of compressor stations, the lengths of pipeline segments between compressor stations, the diameters of the pipeline segments, the suction and discharge pressures at each compressor station. To facilitate the calculation of the design of a pipeline, gas engineers proposed, in several handbooks, to base their cost-assessments on some optimal properties from previous experiences and usual engineering practices: the distance between compressors is constant, all diameters are equal, and all inlet (resp. outlet) pressures are equal. The goals of this paper are (1) to state on which assumptions we can consider that the optimal properties are valid and (2) to propose a rigorous proof of the optimal properties (based on nonlinear programming optimality conditions) within a more general framework than before.
• Minimal Time Problems with Moving Targets and Obstacles
  
  • Bokanowski Olivier
  • Zidani Hasnaa
  , 2011, 18, Part 1, pp.2589-2593. We consider minimal time problems governed by nonlinear systems under general time dependant state constraints and in the two-player games setting. In general, it is known that the characterization of the minimal time function, as well as the study of its regularity properties, is a difficult task in particular when no controlability assumption is made. In addition to these difficulties, we are interested here to the case when the target, the state constraints and the dynamics are allowed to be time-dependent. We introduce a particular "reachability" control problem, which has a supremum cost function but is free of state constraints. This auxiliary control problem allows to characterize easily the backward reachable sets, and then, the minimal time function, without assuming any controllability assumption. These techniques are linked to the well known level-set approachs. Partial results of the study have been published recently by the authors in SICON. Here, we generalize the method to more complex problems of moving target and obstacle problems. Our results can be used to deal with motion planning problems with obstacle avoidance. (10.3182/20110828-6-IT-1002.02261)
  DOI : 10.3182/20110828-6-IT-1002.02261
• Time reversal and scattering theory for time-dependent acoustic waves in a homogeneous medium
  
  • Ben-Amar Chokri
  • Hazard Christophe
  IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2011, 76, pp.938-955.