Helmholtz equation in periodic media with a line defect

Julien Coatléven 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We consider the Helmholtz equation in an unbounded periodic media perturbed by an unbounded defect whose structure is compatible with the periodicity of the underlying media. We exhibit a method coupling Dirichlet-to-Neumann maps with the Lippmann-Schwinger equation approach to solve this problem, where the Floquet-Bloch transform in the direction of the defect plays a central role. We establish full convergence estimates that makes the link between the rate of decay of a function and the good behavior of a quadrature rule to approximate the inverse Floquet-Bloch transform. Finally we exhibit a few numerical results to illustrate the efficiency of the method. © 2011 Elsevier Inc.
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Submitted on : Friday, August 30, 2013 - 11:07:07 AM
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Julien Coatléven. Helmholtz equation in periodic media with a line defect. Journal of Computational Physics, Elsevier, 2012, 231 (4), pp.1675-1704. ⟨10.1016/j.jcp.2011.10.022⟩. ⟨hal-00849565⟩

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