Defect reconstruction in waveguides using resonant frequencies

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Résumé : 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 using a Schrodinger equation satisfied by each mode. Then, we use this approximation to solve the inverse problem: given partial wavefield measurements, we reconstruct width defects in a stable and precise way and provide numerical validations and comparisons with existing methods.