Iterative methods for scattering problems in unbounded elastic waveguides

Vahan Baronian (1) , Anne-Sophie Bonnet-Ben Dhia (2) , Sonia Fliss (2) , Antoine Tonnoir (2)

1 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

We consider the time-harmonic problem of the diffraction of an incident propagative mode by a localized defect, in an infinite straight isotropic elastic waveguide. We propose several iterative algorithms to compute an approximate solution of the problem, using a classical finite element discretization in a small area around the perturbation, and a modal expansion in unbounded straight parts of the guide. Each algorithm can be related to a so-called domain decomposition method, with or without an overlap between the domains. Specific transmission conditions are used, so that only the sparse finite element matrix has to be inverted, the modal expansion being obtained by a simple projection, using the Fraser bi-orthogonality relation. The benefit of using an overlap between the finite element domain and the modal domain is emphasized, in particular for the extension to the anisotropic case. The transparency of these new boundary conditions is checked for two- and three-dimensional anisotropic waveguides. Finally, in the isotropic case, numerical validation for two- and three-dimensional waveguides illustrates the efficiency of the new approach, compared to other existing methods, in terms of number of iterations and CPU time.

Mots clés: elastic waveguide; diffraction; modal expansion; domain decomposition method; iterative methods

Domaines: Equations aux dérivées partielles [math.AP]

Vahan Baronian, Anne-Sophie Bonnet-Ben Dhia, Sonia Fliss, Antoine Tonnoir. Iterative methods for scattering problems in unbounded elastic waveguides. Wave Motion, 2016. ⟨hal-01164794v2⟩