Publications

2026

• A global-in-time domain decomposition approach for transient acoustic-elastic interaction
  
  • Bonnet Marc
  • Chaillat Stéphanie
  • Nassor Alice
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2026. This work develops a global-in-time iterative domain decomposition approach for transient fluid-structure interaction problems involving acoustic scattering by elastic obstacles. The proposed method, inspired by optimized Schwarz waveform relaxation algorithms, proceeds by iteratively exchanging Robin boundary conditions, enabling the non-intrusive coupling of distinct fluid and structure solvers, and allows arbitrary transient incident acoustic fields. We prove the convergence of the proposed coupling iterations in continuous form. A BEM-FEM coupling implementation of the method is then validated against a reference analytical solution, and its efficiency, accuracy and robustness demonstrated through numerical experiments on configurations representative of potential industrial applications.
• Spectral theory for periodic operators
  
  • Fliss Sonia
  , 2026, 67. These lecture notes present the main results on the spectral theory of periodic operators with or without perturbations. After recalling the Floquet Bloch transform and the main results of spectral theory, we prove that periodic operators have a band spectrum with possibly band gaps. We will focus in particular on the so-called SSH discrete operator and 1D differential operators for which explicit computations can be done. We will then show few techniques to create gaps by playing with the coefficients. Finally, we will study the effect of perturbations of the periodic coefficients on the spectrum of the underlying operator. In particular, when the perturbation is localized, some discrete spectrum can appear. These lecture was given during the Research School "Théorie Spectrale, Contrôle et Problèmes inverses" in the framework of the CIRM-SMF Program.