Transparent boundary conditions for locally perturbed infinite hexagonal periodic media
Analysis of PDEs
2012-05-25 v1
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.
Keywords
Cite
@article{arxiv.1205.5345,
title = {Transparent boundary conditions for locally perturbed infinite hexagonal periodic media},
author = {Christophe Besse and Julien Coatleven and Sonia Fliss and Ingrid Lacroix-Violet and Karim Ramdani},
journal= {arXiv preprint arXiv:1205.5345},
year = {2012}
}