Transparent boundary conditions for locally perturbed infinite hexagonal periodic media. - Archive ouverte HAL Access content directly
Journal Articles Communications in Mathematical Sciences Year : 2013

Transparent boundary conditions for locally perturbed infinite hexagonal periodic media.

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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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Dates and versions

hal-00698916 , version 1 (23-05-2012)

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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, 2013, 11 (4), pp.907-938. ⟨hal-00698916⟩
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