Publications

Titre : Augmented Galerkin schemes for the numerical solution of scattering by small obstacles
Année : 2007
Type : rapport de recherche
Auteurs : X. Claeys, F. Collino
Résumé : In the context of electromagnetic wave propagation, we wish to adress the scattering problem from perfectly conducting thin wires. For numerical simulations, assuming their thickness to be much smaller than the wavelength of the incident field, it is not possible to take these obstacles into account without encountering problems of numerical locking.\\ \quad The Holland model, widely used in finite difference schemes, provides a pragmatic solution to this problem, by modifying the numerical scheme on vertices located in the neighbourhood of the wires. So far this model has not received any real theoretical justification, and involves a parameter, named lineic inductance, which is to be chosen on the basis of heuristic considerations.\\ \quad We are interested in the simplified problem of a bidimensional acoustic wave propagation in a medium including a small obstacle with homogeneous Dirichlet boundary condition. We present and analyse a numerical scheme suitable for finite elements that does not suffer from numerical locking, and takes the presence of the small obstacle into account. It is based on a combination between the fictitious domain method and matched asymptotic expansions. This results into a systematic generalization to the Holland model including an automatic computation of the lineic inductance. Our analysis leads to the first (to our knowledge) justification of this type of model.
Thèmes :
Référence : images/icons/doctype_pdf.gif