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A volume integral method for solving scattering problems from locally perturbed infinite periodic layers

Houssem Haddar 1 Thi Phong Nguyen 1
1 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : We investigate the scattering problem for the case of locally perturbed periodic layers in $\R^d$, $d=2,3$. Using the Floquet-Bloch transform in the periodicity direction we reformulate this scattering problem as an equivalent system of coupled volume integral equations. We then apply a spectral method to discretize the obtained system after periodization in the direction orthogonal to the periodicity directions of the medium. The convergence of this method is established and validating numerical results are provided.
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Houssem Haddar, Thi Phong Nguyen. A volume integral method for solving scattering problems from locally perturbed infinite periodic layers. Applicable Analysis, Taylor & Francis, 2016, pp.29. ⟨10.1080/00036811.2016.1221942⟩. ⟨hal-01374892⟩

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