Fast Boundary Elements Methods for time-harmonic high-frequency wave propagation problems

In this talk, Marion Darbas will present results related to the numerical resolution of time-harmonic high-frequency wave propagation problems using the boundary integral equation method.

First,  she will discuss results obtained over the past few years, focusing on the construction of analytic preconditioners and the associated well-conditioned boundary integral equations for solving exterior problems. We will see how local approximations of the Dirichlet-to-Neumann map play a crucial role in enabling efficient fast solvers.

Next, she will present on-going work dedicated to the derivation of multitrace boundary integral formulations for elastic transmission problems. These researches are part of an ECOS Sud-Chile project. This is a joint work with Stéphanie Chaillat (CNRS-INRIA-ENSTA POEMS team, France), Paul Escapil-Inchauspé (Inria Chile) and Carlos Jerez-Hanckes (Universidad Adolfo Ibáñez, Chile).

Marion Darbas is a full professor in applied mathematics at the LAGA laboratory, Université Sorbonne-Paris-Nord, since 2020. Her research is focusing on the modeling and numerical resolution of direct and inverse wave propagation problems. She is interested in medical applications in particular.

In this talk, she will present results related to the numerical resolution of time-harmonic high-frequency wave propagation problems using the boundary integral equation method.