Defect reconstruction in waveguides using resonant frequencies (Angèle Niclas, École Polytechnique)Séminaire « Analyse numérique et équations aux dérivées partielles »
This talk aims at introducing a new multi-frequency method to reconstruct width defects in waveguides. Different inverse methods already exist. However, those methods are not using some frequencies, called resonant frequencies, where propagation equations
are known to be ill-conditioned. Since waves seem very sensible to defects at these particular frequencies, we exploit them instead. After studying the forward problem at these resonant frequencies, we approximate the wavefield and focus on the inverse problem. Given partial wavefield measurements, we reconstruct slowly varying width defects in a stable and precise way and provide numerical validations and comparisons with existing methods.