PDE and applications seminar | Nancy - Institut Élie Cartan de Lorraine

Upcoming presentations

Spectral approach for an homogenization problem using boundary integral operators

Catégorie d'évènement : Séminaire Équations aux Derivées Partielles et Applications (Nancy) Date/heure : 9 June 2026 10:45-11:45 Lieu : Salle de conférences Nancy Oratrice ou orateur : Anthony GERBER-ROTH Résumé :

A problem in electrostatic in the context of homogenization is studied. Assuming that each phase is made of a material with constant conductivity, we show that an approach based on boundary integral operators associated to the interfaces between the phases can be used. An introduction to such operators in the context of periodic conditions is presented. The problem is then showed to be equivalent to a boundary integral equation involving the so-called Neumann-Poincaré operator. As a consequence, its spectral properties can be used in order to derive an explicit modal expansion formula for the solution to the problem. The approach will be compared with the one involving the so-called Lippmann-Schwinger operator which is more systematically used in this context. In addition, the eigenpairs involved in the expansion are explored numerically and their links with those of the Lippmann-Schwinger operator are discussed.