Publications

2011

• Strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions
  
  • Graber Philip Jameson
  Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2011, 74, pp.3137-3148. We consider a wave equation with semilinear porous acoustic boundary conditions. This is a coupled system of second and first order in time partial differential equations, with possibly semilinear boundary conditions on the interface. The results obtained are (i) strong stability for the linear model, (ii) exponential decay rates for the energy of the linear model, and (iii) local exponential decay rates for the energy of the semilinear model. This work builds on a previous result showing generation of a well-posed dynamical system. The main tools used in the proofs are (i) the Stability Theorem of Arendt-Batty, (ii) energy methods used in the study of a wave equation with boundary damping, and (iii) an abstract result of I. Lasiecka applicable to hyperbolic-like systems with nonlinearly perturbed boundary conditions. (10.1016/j.na.2011.01.029)
  DOI : 10.1016/j.na.2011.01.029
• 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.
• 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
• 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
• Compact imbeddings in electromagnetism with interfaces between classical materials and meta-materials
  
  • Chesnel Lucas
  • Ciarlet Patrick
  , 2011. In a meta-material, the electric permittivity and/or the magnetic permeability can be negative in given frequency ranges. We investigate the solution of the time-harmonic Maxwell equations in a composite material, made up of classical materials, and meta-materials with negative electric permittivity, in a two-dimensional bounded domain Ω. We study the imbedding of the space of electric fields into L²(Ω)². In particular, we extend the famous result of Weber, proving that it is compact. This result is obtained by studying the regularity of the fields. We first isolate their most singular part, using a decomposition à la Birman-Solomyak. With the help of the Mellin transform, we prove that this singular part belongs to Hˢ(Ω)², for some s > 0. Finally, we show that the compact imbedding result holds as soon as no ratio of permittivities between two adjacent materials is equal to −1.
• 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.
• Application of convex lexicographical optimization to the balance of GRTgaz gas grid
  
  • Bonnans Joseph Frederic
  • Paraisy Ruben
  • Veyrat Sébastien
  • Adam Soizic
  Journal of Global Optimization, Springer Verlag, 2011, 49 (3), pp.415--423.
• Mathematical and numerical modelling of wave propagation in fractal trees
  
  • Joly Patrick
  • Semin Adrien
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2011.
• On stochastic calculus related to financial assets without semimartingales
  
  • Coviello Rosanna
  • Di Girolami Cristina
  • Russo Francesco
  Bulletin des Sciences Mathématiques, Elsevier, 2011, 135, pp.733-774. This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class $\mathcal{A}$ of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of $\mathcal{A}$-martingale. A calculus related to $\mathcal{A}$-martingales with some examples is developed. Some applications to no-arbitrage, viability, hedging and the maximization of the utility of an insider are expanded. We finally revisit some no arbitrage conditions of Bender-Sottinen-Valkeila type. (10.1016/j.bulsci.2011.06.008)
  DOI : 10.1016/j.bulsci.2011.06.008
• An alternative to Dirichlet-to-Neumann maps for waveguides
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Legendre Guillaume
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2011, 349 (17-18), pp.1005-1009. We are interested by the treatment of the radiation condition at infinity for the numerical solution of a problem set in an unbounded waveguide. We propose an alternative to the classical approach involving a modal expression of Dirichlet-to-Neumann (DtN) operators. This method is particularly simple to implement since it only requires the solution of boundary value problems with local boundary conditions. The corresponding approximate solution is comparable in accuracy to the one obtained by truncating the infinite series in the DtN maps. (10.1016/j.crma.2011.08.006)
  DOI : 10.1016/j.crma.2011.08.006
• Minimum d-blockers and d-transversals in graphs
  
  • Costa Marie-Christine
  • de Werra Dominique
  • Picouleau Christophe
  Journal of Combinatorial Optimization, Springer Verlag, 2011, 22 (4), pp.857-872. We consider a set V of elements and an optimization problem on V : the search for a maximum (or minimum) cardinality subset of V verifying a given property P. A d-transversal is a subset of V which intersects any optimum solution in at least d elements while a d-blocker is a subset of V whose removal deteriorates the value of an optimum solution by at least d. We present some general characteristics of these problems, we review some situations which have been studied (matchings, s . t paths and s . t cuts in graphs) and we study d-transversals and d-blockers for new problems as stable sets or vertex covers in bipartite graphs. (10.1007/s10878-010-9334-6)
  DOI : 10.1007/s10878-010-9334-6
• Non-reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow
  
  • Redon Emmanuel
  • Bonnet-Ben Dhia Anne-Sophie
  • Mercier Jean-François
  • Sari Poernomo
  International Journal for Numerical Methods in Engineering, Wiley, 2011, 86 (11), pp.1360-1378. We consider a time-harmonic acoustic scattering problem in a 2D infinite waveguide with walls covered with an absorbing material, in the presence of a mean flow assumed uniform far from the source. To make this problem suitable for a finite element analysis, the infinite domain is truncated. This paper concerns the derivation of a non-reflecting boundary condition on the artificial boundary by means of a Dirichlet-to-Neumann (DtN) map based on a modal decomposition. Compared with the hard-walled guide case, several difficulties are raised by the presence of both the liner and the mean flow. In particular, acoustic modes are no longer orthogonal and behave asymptotically like the modes of a soft-walled guide. However, an accurate approximation of the DtN map can be derived using some bi-orthogonality relations, valid asymptotically for high-order modes. Numerical validations show the efficiency of the method. The influence of the liner with or without mean flow is illustrated. (10.1002/nme.3108)
  DOI : 10.1002/nme.3108