Transparent boundary conditions for locally perturbed infinite hexagonal periodic media
Abstract
In this paper, we propose a strategy to determine the DirichlettoNeumann (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 halfspace problem. The second one is a DirichlettoDirichlet (DtD) type operator related to the symmetry properties of the problem. The halfspace DtN operator is characterized via FloquetBloch 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 DOI:
 10.48550/arXiv.1205.5345
 arXiv:
 arXiv:1205.5345
 Bibcode:
 2012arXiv1205.5345B
 Keywords:

 Mathematics  Analysis of PDEs