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Transparent boundary conditions for locally perturbed infinite hexagonal periodic media.

Christophe Besse 1, 2, * Julien Coatleven 3, 4 Sonia Fliss 3, 4 Ingrid Lacroix-Violet 1, 2 Karim Ramdani 5, 6
* Corresponding author
2 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
4 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
5 CORIDA - Robust control of infinite dimensional systems and applications
IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est
Abstract : In this paper, we propose a strategy to determine the Dirichlet-to-Neumann (DtN) operator for infinite, lossy and locally perturbed hexagonal periodic media. We obtain a factorization of this operator involving two non local operators. The first one is a DtN type operator and corresponds to a half-space problem. The second one is a Dirichlet-to-Dirichlet (DtD) type operator related to the symmetry properties of the problem. The half-space DtN operator is characterized via Floquet-Bloch transform, a family of elementary strip problems and a family of stationary Riccati equations. The DtD operator is the solution of an affine operator valued equation which can be reformulated as a non standard integral equation.
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Submitted on : Wednesday, May 23, 2012 - 3:46:50 PM
Last modification on : Friday, December 3, 2021 - 11:34:08 AM
Long-term archiving on: : Thursday, December 15, 2016 - 9:34:46 AM


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  • HAL Id : hal-00698916, version 1
  • ARXIV : 1205.5345


Christophe Besse, Julien Coatleven, Sonia Fliss, Ingrid Lacroix-Violet, Karim Ramdani. Transparent boundary conditions for locally perturbed infinite hexagonal periodic media.. Communications in Mathematical Sciences, International Press, 2013, 11 (4), pp.907-938. ⟨hal-00698916⟩



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