SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2007-2008
Jeudi 8 novembre 2007 :
Xavier CLAEYS
(INRIA Rocquencourt)
Justification théorique de l'équation de Pocklington
pour la diffraction par des fils minces
Pocklington's model consists in a simplified one-dimensional integral equation relating the current at the surface of a thin straight finite wire to the tangential trace of an incident electromagnetic field. This simplified equation has been proved to be well posed. However, to our knowledge, there has been no study of the error between the solution of the exact two-dimensional integral equation and the solution of Pocklington's equation. We address this problem for the model case of acoustics in a smooth geometry. Our approach is based on three main ingredients: asymptotic analysis, a mixed formulation of the problem, and the introduction of an averaging operator.