Jeffrey Rauch (University of Michigan)
Reports on the construction of absorbing layers for the one dimensional linearized water wave equation. The equation is nonlocal forcing it immediately out of the realm of standard ideas. A key and simple is idea is one way water wave equations related to D'Alembert's method. Joint work with Izbicki, Karni, Carney, Abgrall, and Prigge (in chronological order).
Jean-Claude Nedelec (CMAP Polytechnique)
We introduce four integral operators closely related to the Laplace equation in three-dimensions on the circular unit disc. Two of them are closed to the simple layer on the disc and the other two are related to the hyper singular operator. Contrary to the case of a closed domain, these operators no longer map fractional Sobolev spaces in a dual fashion but degenerate into different subspaces...
Nick TERFETHEN (University of Oxford)
Everybody has heard of the Faraday cage effect, in which a wire mesh does a good job of blocking electric fields. Surely the mathematics of such a famous and useful phenomenon has been long ago worked out and written up in the textbooks? It seems to be not so. One reason may be that that the effect is not as simple as one might expect: it depends on the wires having finite radius. ...
We consider Hamiltonians with cutoffs which are self-adjoint operators in appropriate Fock spaces with a unique ground state. A limiting Absorbtion Principle is proved
In order to control locally a space-time which satisfies the Einstein equations, what are the minimal assumptions one should make on its curvature tensor? The bounded L2 curvature conjecture roughly asserts that one should only need L2 bounds of the curvature tensor on a given space-like hypersurface. This conjecture has its roots in the remarkable developments of the last twenty years...
Yann Brenier (CMLS École Polytechnique)
In the 1990, Moffatt discussed a dissipative model of Magneto-hydrodynamics (that he called “magnetic relaxation” but could also be called “Darcy” or “Stokes” MHD), in order to get stationary solutions of the Euler equations with prescribed topology. We will discuss the corresponding PDEs and some concepts of generalized solutions related both to P.-L. Lions’ dissipative solutions to...
Patrick Joly (INRIA)
We consider the propagation of waves in a periodic structure that can be represented as a infinite thick graph. We show that, provided that adequate boundary conditions are satisfied, the introduction of a lineic geometric perurbation of this reference structure can create the apparition of guided waves associated to frequencies inside any band gap of the periodic medium. The proof is...
We introduce the time reversed absorbing conditions (TRAC) in time reversal methods. They enable to ``recreate the past'' without knowing the source which has emitted the signals that are back-propagated. The method is very insensitive to noise in the data. Applications to coefficients reconstruction and source identification are given.
Abderrahmane BENDALI (INSA Toulouse)
Usual Foldy's model is used to approximate a multiple scattering problem involving small scatterers by monopole scatterers. Using the method of matched asymptotic expansions, with P. H. Cocquet and S. Tordeux, we have first proved that the scattered field can be approximated at any order of accuracy by multipoles. This first provides a mathematical justification for the Foldy model and...
Marc Schoenauer (INRIA)
Optimisation is concerned with finding the arguments that result in the largest (or lowest) value of some objective function. However, whereas the range and scale of possible values of the objective function is often arbitrary, the performance of optimisation algorithms very often heavily depends on the chosen coordinates. Comparison-based methods can hence get an edge...
Jean-Jacques Marigo (LMS École Polytechnique)
It is well-accepted that Griffith-like models are appropriate for crack propagation at the scale of a structure, but inadequate for the modeling of crack nucleation in brittle materials. Arguably, finer models, where a microscopic (material) length scale plays a fundamental role, are necessary to determine the critical load and crack geometry at the onset. The consistent combined modeling and...
19. Adaptive time stepping and Schwarz Waveform Relaxation (SWR) Method for Compressible Navier–Stokes Equations
Oana Ciobanu (Paris 13 et Onera)
A space-time domain decomposition algorithm for the compressible Navier–Stokes problem has been designed, with the aim of implementing it in three dimensions, in an industrial code. We improve the SWR method adding an adaptive time stepping inside each time window and compare its performances for different second order explicit/implicit algorithms, on complexe cases.
In this talk we show how numerical models and algorithms can be tailored to HPC platforms to address multiscale problems occurring in turbulent transport.
Soheil HAJIAN (Université de Genève)
Domain decomposition preconditioners and in particular the additive Schwarz method are favorite preconditioners for classical finite element methods (FEM). There is a huge effort in designing similar preconditioners for discontinuous Galerkin (DG) discretizations. It has been shown that additive Schwarz methods use different mechanisms for convergence when applied to a DG discretization...
28. Analyse d'erreur a posteriori et raffinement auto-adaptatif pour les éléments finis de frontière en acoustique
Marc Bakri (ONERA)
Nous présenterons plusieurs indicateurs d'erreur /a posteriori /adaptés aux méthodes d'éléments finis utilisées pour discrétiser les équations intégrales en acoustique 2D. En particulier, nous introduirons une nouvelle classe d'estimateurs fiables et efficaces dont la construction est basée sur une nouvelle technique de localisation des normes de Sobolev fractionnaires.
30. Comparison of Neuman-Neuman and Optimal Schwarz Methods with Many Subdomains in one Spatial Dimensions
Faycal Chaouqui (Université de Genève)
Optimal Schwarz methods and Neuman-Neuman methods have for two subdomains both the interesting property that they can lead to nil-potent iteration matrices. We study in this poster if this property can also be obtained for the case of a strip decomposition into many subdomains. We show that only the optimal Schwarz method can lead in this case to a nil-potent iteration matrix, and that...
Mrs imen hassairi (Did not come to the conference)
We are concerned with the problem of existence and uniqueness of a solution in class D for the backward stochastic differential equations (BSDEs for short) with two continuous reflecting barriers which are completely separated. We consider that the data are Lp-integrable with p = 1.
Hui Zhang (Université de Genève)
Many of the modern iterative algorithms for the Helmholtz (or a more general PDE) operator have common ingredients. We show that all these algorithms can be understood in the framework of optimized Schwarz methods. They only differ in the particular choice on how to approximate the optimal transmission condition which contains a Dirichlet to Neumann operator, in the choice of the subdomain...
Asma Toumi (ONERA)
La simulation numérique est de systèmes physiques multi-échelles est souvent synonyme de calculs coûteux et particulièrement longs. En effet, dans les méthodes classiques d’intégration temporelle, le pas de temps local le plus faible est souvent limitant pour le pas de temps global d'intégration. Notre étude porte sur un schéma asynchrone permettant de lever cette limitation. Ce formalisme...
31. Space-time domain decomposition methods for mixed formulations of flow and transport problems in porous media
Flow and transport problems in porous media are well-known for their high computational cost. In the simulation of an underground nuclear waste disposal site, one has to work with extremely different length and time scales, and highly variable coefficients while satisfying strict accuracy requirements. One strategy for tackling these difficulties is to apply a non-overlapping domain...
Mr Zakaria Belhaj (Did not come to the conference)
Troesch's problem arises in the investigation of the confinement of a plasma column by radiation pressure. Recently, this problem has been studied extensively. We present a variational approximation method for solving Troesch's problem. The existence and the uniqueness of this problem are shown. Moreover, we construct a sequence of solutions of the problem from the number of knots in the...
34. Wave-Ray Multigrid Method for The 1D Helmholtz Equation A precise mathematical formulation and first analysis
Shu-Lin Wu (Université de Genève)
We try to analyze the convergence properties of the wave-ray multigrid method for the Helmholtz equation in the 1D case. We present the details of the method and perform a local Fourier analysis for the convergence behavior. This preliminary study shows no remarkable evidence of advantages by using the wave-ray idea.
Pierre Degond (Imperial College London)
Collective dynamics refers to the ability of motile agents to achieve large-scale coordination through purely local interactions. Systems exhibiting collective dynamics can be found in the living world (motor proteins, cells, birds, pedestrians) as well as in the social world (opinion, wealth). Collective dynamics challenges the existing theories relating microscopic to macroscopic...
Mohamed Amara (Université de Pau)
the presentation deals about a procedure for selecting basis function orientation to improve the e?fficiency of solution methodologies that employ local plane-wave approximations. The proposed adaptive approach consists of a local wave tracking strategy. Each plane-wave basis set within considered elements of the mesh partition is individually or collectively rotated to best align one...