English

Symbol of the Dirichlet-to-Neumann operator in 2D diffraction problems with large wavenumber

Optics 2007-05-23 v1 Computational Physics

Abstract

We put forward a conjecture about an universal asymptotical behaviour of the symbol of the Dirichlet-to-Neumann operator (considered as a pseudodifferential operator) in the 2D exterior problem for the Hemholtz equation. The conjecture is motivated by simple explicit examples and backed by numerical calculations, even in the case of a non-convex obstacle. It implies (at a physical level of rigor) Kirhhoff's approximation.

Keywords

Cite

@article{arxiv.physics/0310048,
  title  = {Symbol of the Dirichlet-to-Neumann operator in 2D diffraction problems with large wavenumber},
  author = {Margarita F. Kondratieva and Sergey Yu. Sadov},
  journal= {arXiv preprint arXiv:physics/0310048},
  year   = {2007}
}

Comments

10 pages, 4 figures, LaTeX/ps, talk at the conference "Days on Diffractions'03", St.Petersburg, Russia, June 2003