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

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

2003-10-10

arxiv.org/abs/physics/0310048v1

Physics

Optics

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

Scientific paper

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.

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