Transparent boundary conditions for locally perturbed infinite hexagonal periodic media

2012/05/24 by Christophe Besse, Besse, Christophe, Julien Coatléven +9
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Photonic Crystals and Applications #math.AP

paper · pdf · doi:10.48550/arxiv.1205.5345

arxiv created 2012/05/24 · openalex publication_date 2012/05/24 · arxiv updated 2012/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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