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Transparent boundary conditions for the harmonic diffraction problem in an elastic waveguide

Vahan Baronian 1 Anne-Sophie Bonnet-Ben Dhia 1 Éric Lunéville 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : This work concerns the numerical finite element computation, in the frequency domain, of the diffracted wave produced by a defect (crack, inclusion, perturbation of the boundaries, etc.) located in a 3D infinite elastic waveguide. The objective is to use modal representations to build transparent conditions on some artificial boundaries of the computational domain. This cannot be achieved in a classical way, due to non-standard properties of elastic modes. However, a biorthogonality relation allows us to build an operator, relating hybrid displacement/stress vectors. An original mixed formulation is then derived and implemented, whose unknowns are the displacement field in the bounded domain and the normal component of the normal stresses on the artificial boundaries. Numerical validations are presented in the 2D case.
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Submitted on : Monday, April 7, 2014 - 5:57:07 PM
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Vahan Baronian, Anne-Sophie Bonnet-Ben Dhia, Éric Lunéville. Transparent boundary conditions for the harmonic diffraction problem in an elastic waveguide. Journal of Computational and Applied Mathematics, Elsevier, 2010, 234 (6), pp.1945-1952. ⟨10.1016/⟩. ⟨hal-00975075⟩



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