Publications

2002

• Le partage de secret
  
  • Loidreau Pierre
  MISC - Le journal de la sécurité informatique, Lavoisier, 2002, 3.
• Theoretical tools to solve the axisymmetric Maxwell equations
  
  • Assous Franck
  • Ciarlet Patrick
  • Labrunie Simon
  Mathematical Methods in the Applied Sciences, Wiley, 2002, 25 (1), pp.49-78. In this paper, the mathematical tools, which are required to solve the axisymmetric Maxwell equations, are presented. An in-depth study of the problems posed in the meridian half-plane, numerical algorithms, as well as numerical experiments, based on the implementation of the theory described hereafter, shall be presented in forthcoming papers. In the present paper, the attention is focused on the (orthogonal) splitting of the electromagnetic field in a regular part and a singular part, the former being in the Sobolev space H-1 component-wise. It is proven that the singular fields are related to singularities of Laplace-like operators, and, as a consequence, that the space of singular fields is finite dimensional. Copyright (C) 2002 John Wiley Sons, Ltd. (10.1002/mma.279)
  DOI : 10.1002/mma.279
• A Direct Study in a Hilbert-Schmidt Framework of the Riccati Equation Appearing in a Factorization Method of Second Order Elliptic Boundary Value Problems
  
  • Henry Jacques
  • Ramos Angel M.
  , 2002. In this report we come back to the method of factorization of a second order elliptic boundary value problem presented in . In this paper, it was shown that, in the case of a cylinder, the boundary value problem can be factorized in two uncoupled first order initial value problems. This factorization utilizes the Dirichlet to Neumann operator which satisfies a Riccati equation. Here we consider Hilbert-Schmidt operators, a framework already used by R. Temam which provides tools for a direct study of this Riccati equation.
• A singular field method for Maxwell's equations: numerical aspects for 2D magnetostatics
  
  • Hazard Christophe
  • Lohrengel Stéphanie
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2002, 40 (3), pp.1021--1040. The present paper deals with the solution of Maxwell-type problems by means of nodal H1-conforming finite elements. In a nonconvex piecewise regular domain surrounded by a perfect conductor, such a discretization cannot in general approximate the singular behavior of the electromagnetic field near "reentrant" corners or edges. The singular field method consists of adding to the finite element discretization space some particular fields which take into account the singular behavior. The latter are deduced from the singular functions associated with the scalar Laplace operator.The theoretical justification of this approach as well as the analysis of the convergence of the approximation are presented for a very simple model problem arising from magnetostatics in a translation invariant setting, but the study can be easily extended to numerous Maxwell-type problems. The numerical implementation of both variants is studied for a domain containing a single reentrant corner. (10.1137/S0036142900375761)
  DOI : 10.1137/S0036142900375761
• Measures of Sub-Riemannian Paths
  
  • Jean Frédéric
  • Falbel Elisha
  , 2002.