Research topics
Main research topics
- Obtaining asymptotically effective models for wave propagation. The aim is to take into account the presence of thin layers, small heterogeneities or microstructures of the medium, in an approximate model that is less costly to solve numerically than the initial model obtained by techniques such as connected asymptotic expansion or double-scale homogenization.
- Applications of spectral theory to the analysis of wave propagation. We are particularly interested in the study of waveguides, whether closed or open, uniform or periodic. Depending on the case, the aim is to prove the existence of gaps in the essential spectrum, and the existence or non-existence of eigenvalues in the gaps or dips in the essential spectrum.
- The development of specific methods for the treatment of wave propagation or diffraction in unbounded domains. We develop methods for transparent or absorbing conditions (Dirichlet-to-Neumann, Perfectly Matched Layers) as well as integral methods.
- Design and implementation of efficient numerical methods for wave propagation. In particular, we develop domain decomposition approaches and Fast Multipole Method (FMM) and H-Matrix methods for integral equations.
- Inverse Diffraction Problems: The goal is to detect and/or identify objects based on the measurement of the far field diffracted by these objects when illuminated by an incident wave. In particular, we develop sampling methods based on the concepts of linear sampling or topological gradient.
Main application areas
- The study of electromagnetic wave propagation in non-classical media such as metamaterials or plasmas. For example, we are interested in the design of stable PML layers in dispersive media.
- Simulation of elastic wave propagation in the subsurface. The aim is to study site effects (amplification of seismic motion by topography, geological structure, etc.) or soil-structure interactions.
- Sound propagation in a flow. This subject, which is part of the field of aeroacoustics, is involved in efforts to reduce aircraft noise.
- Non-destructive testing of structures using ultrasonic waves. We are particularly interested in NDT of guide structures such as pipes or plates.
