Matthieu Gallezot, Forward models based on a modal approach for fast topological imaging of open elastic waveguides

This talk presents numerical models of the propagation and the diffraction of waves in open waveguides, i.e. with an unbounded cross-section. These structures are widely encountered in civil engineering (embedded rock bolts, buried pipes...). The models are based on modal decompositions of the source or at the boundaries of a finite element box enclosing a diffracting object. I first recall that guided modes are solutions of an eigenvalue problem written on the waveguide's cross-section truncated with a perfectly matched layer (PML). To guarantee the uniqueness of the modal expansions, an orthogonality relationship is derived. I then detail the complicated nature of the modal basis in open waveguides, and how it is modified when a perfectly matched layer (PML) is introduced in the transverse direction. Through several numerical test cases, I discuss whether and how the modal expansions can be truncated to reduce the computational cost. Finally, these models are combined to efficiently simulate topological imaging of open waveguides. The imaging function is the topological energy computed from the forward and adjoint fields, which are solutions of the forced response problem (same solver with two different sources). The synthetic diffracted field is obtained using both the forced response and the diffraction model.