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

2003/10/10 by Margarita F. Kondratieva, Sergey Sadov, Kondratieva, Margarita F. +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #FOS: Physical sciences #Numerical methods in inverse problems #Optics (physics.optics) #physics.comp-ph #physics.optics

paper · pdf · doi:10.48550/arxiv.physics/0310048

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

arxiv created 2003/10/10 · openalex publication_date 2003/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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