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

Авторы: Kondratieva M.F., Sadov S.Yu
Сборник: International Seminar Day on Diffraction, 2003. Proceedings
Год издания: 2003
Место издания: IEEE
Первая страница: 88
Последняя страница: 98
DOI: 10.1109/DD.2003.238180
Аннотация: Consider the Dirichlet-to-Neumann operator N in the exterior problem for the 2D Helmholtz equation outside a bounded domain with smooth boundary. Using parametrization of the boundary by normalized arclength, we treat N as a pseudodifferential operator on the unit circle. We study its discrete symbol. We put, forward a conjecture on the universal behaviour, independent of shape and curvature of the boundary, of the symbol as the wavenumber k tends to infinity. The conjecture is motivated by an explicit formula for circular boundary, and confirmed numerically for other shapes. It also agrees, on a physical level of rigor, with Kirchhoff's approximation. The conjecture, if true, opens new ways in numerical analysis of diffraction in the range of moderately high frequencies.
Добавил в систему: Садов Сергей Юрьевич

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