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Approximate local Dirichlet-to-Neumann map for three-dimensional time-harmonic elastic waves

Abstract : It has been proven that the knowledge of an accurate approximation of the Dirichlet-to-Neumann (DtN) map is useful for a large range of applications in wave scattering problems. We are concerned in this paper with the construction of an approximate local DtN operator for time-harmonic elastic waves. The main contributions are the following. First, we derive exact operators using Fourier analysis in the case of an elastic half-space. These results are then extended to a general three-dimensional smooth closed surface by using a local tangent plane approximation. Next, a regularization step improves the accuracy of the approximate DtN operators and a localization process is proposed. Finally, a first application is presented in the context of the On-Surface Radiation Conditions method. The efficiency of the approach is investigated for various obstacle geometries at high frequencies.
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Submitted on : Thursday, August 27, 2015 - 5:02:29 PM
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Stéphanie Chaillat, Marion Darbas, Frédérique Le Louër. Approximate local Dirichlet-to-Neumann map for three-dimensional time-harmonic elastic waves. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, 297 (1), pp.62-83. ⟨10.1016/j.cma.2015.08.013⟩. ⟨hal-01187242⟩

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