Publications

2003

• Some observations on generalized saddle-point problems
  
  • Ciarlet Patrick
  • Huang Jianguo
  • Zou Jun
  SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2003, 25 (1), pp.224-236. This paper studies the solvability and stability of a generalized saddle-point system in finite- and infinite-dimensional spaces. Sharp solvability conditions and stability estimates are derived. Copyright © 2003 Society for Industrial and Applied Mathematics (10.1137/S0895479802410827)
  DOI : 10.1137/S0895479802410827
• An Analysis of Higher Order Boundary Conditions for the Wave Equation.
  
  • Diaz Julien
  • Joly Patrick
  , 2003. Thanks to the use of the Cagniard-De Hoop method, we derive an analytic solution in the time domain for the half-space problem associated with the wave equation with Engquist-Majda higher order boundary conditions. This permits us to derive new convergence results when the order of the boundary condition tends to infinity, as well as error estimates. The theory is illustrated by numerical results.
• Perfectly matched layers for the convected Helmholtz equation
  
  • Bécache Eliane
  • Bonnet-Ben Dhia Anne-Sophie
  • Legendre Guillaume
  , 2003. In this paper, we propose and analyze perfectly matched absorbing layers for a problem of time harmonic acoustic waves propagating in a duct in presence of a uniform flow. The absorbing layers are designed for the pressure field, satisfying the convected scalar Helmholtz equation. A difficulty, compared to the Helmholtz equation, comes from the presence of so-called inverse upstream modes which become unstable, instead of evanescent, with the classical Bérenger's PMLs. We introduce here a new PML model which makes all outgoing waves evanescent. We then analyse the error due to the truncation of the domain and prove that the convergence is exponential with respect to the size of the layers, for both the classical and the new PML models. Numerical validations are finally presented.