Xavier Claeys

Bio: Xavier Claeys is an academic researcher from Paris Diderot University. The author has contributed to research in topics: Helmholtz equation & Domain decomposition methods. The author has an hindex of 12, co-authored 70 publications receiving 564 citations. Previous affiliations of Xavier Claeys include University of Toulouse & University of Paris.

Emergency Braking Control with an Observer-based Dynamic Tire/Road Friction Model and Wheel Angular Velocity Measurement

Abstract: Summary A control scheme for emergency braking of vehicles is designed. The tire/road friction is described by a LuGre dynamic friction model. The control system output is the pressure in the master cylinder of the brake system. The controller utilizes estimated states for a feedback control law that achieves a near maximum deceleration. The state observer is designed using linear matrix inequality (LMI) techniques. The analysis shows that using the wheel angular speed information exclusively is not sufficient to rapidly estimate the velocity and relative velocity, due to the fact that the dynamical system is almost unobservable with this measurement as output. Findings are confirmed by simulation results that show that the estimated vehicle velocity and relative velocity converge slowly to their true values, even though the internal friction state and friction parameters converge quickly. The proposed control system has two main advantages when compared with an antilock braking system (ABS): (1) it produ...

Radiation condition for a non-smooth interface between a dielectric and a metamaterial

Abstract: We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models an ideal metamaterial. When the interface between the two media has a corner, according to the value of the contrast (ratio) of the physical constants, this non-coercive problem can be ill-posed (not Fredholm) in H1. This is due to the degeneration of the two dual singularities which then behave like r±iη = e±iη ln r with η ∈ ℝ*. This apparition of propagative singularities is very similar to the apparition of propagative modes in a waveguide for the classical Helmholtz equation with Dirichlet boundary condition, the contrast playing the role of the wavenumber. In this work, we derive for our problem a functional framework by adding to H1 one of these propagative singularities. Well-posedness is then obtained by imposing a radiation condition, justified by means of a limiting absorption principle, at the corner between the two media.

Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation

Abstract: Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderon identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic scattering at general penetrable composite obstacles. We propose a new first-kind boundary integral equation formulation following the reasoning employed in (X. Clayes and R. Hiptmair, Report 2011-45, SAM, ETH Zurich (2011)) for acoustic scattering. We call itmulti-trace formulation, because its unknowns are two pairs of traces on interfaces in the interior of the scatterer. We give a comprehensive analysis culminating in a proof of coercivity, and uniqueness and existence of solution. We establish a Calderon identity for the multi-trace formulation, which forms the foundation for operator preconditioning in the case of conforming Galerkin boundary element discretization.

High order asymptotics for wave propagation across thin periodic interfaces

Abstract: This work deals with the scattering of acoustic waves by a thin ring that contains many regularly-spaced heterogeneities. We provide and justify a complete description of the solution with respect to the period and the thickness of the heterogeneities. Our approach mixes matched asymptotic expansions and homogenization theory.

Novel Multi-Trace Boundary Integral Equations for Transmission Boundary Value Problems

Abstract: We consider scalar 2nd-order transmission problems in the exterior of a bounded domainΩZ ⊂ R. The coefficients are assumed to be piecewise constant with respect to a partition ofR \ ΩZ into subdomains. Dirichlet boundary conditions are imposed on ∂ΩZ . We recast the transmission problems into two novel well-posed multi-trace boundary integral equations. Their unknowns are functions on the product of subdomain boundaries. Compared to conventional single-trace formulations they offer the big benefit of being amenable to operator preconditioning. We outline the analysis of the new formulations, give the detail s of operator preconditioning applied to them, and, for one type of a multi-trace formulation, report numerical tests confirming the efficacy of operator preconditioning.

A Theory of Graphs

Abstract: A graph is just a bunch of points with lines between some of them, like a map of cities linked by roads. A rather simple notion. Nevertheless, the theory of graphs has broad and important applications, because so many things can be modeled by graphs. For example, planar graphs — graphs in which none of the lines cross are— important in designing computer chips and other electronic circuits. Also, various puzzles and games are solved easily if a little graph theory is applied.

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering ∗

Abstract: In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods