dorsal/arxiv
View SchemaSymbol of the Dirichlet-to-Neumann operator in 2D diffraction problems with large wavenumber
| Authors | Margarita F. Kondratieva, Sergey Yu. Sadov |
|---|---|
| Categories | |
| ArXiv ID | physics/0310048 |
| URL | https://arxiv.org/abs/physics/0310048 |
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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"abstract": "We put forward a conjecture about an universal asymptotical behaviour of the\nsymbol of the Dirichlet-to-Neumann operator (considered as a pseudodifferential\noperator) in the 2D exterior problem for the Hemholtz equation. The conjecture\nis motivated by simple explicit examples and backed by numerical calculations,\neven in the case of a non-convex obstacle. It implies (at a physical level of\nrigor) Kirhhoff\u0027s approximation.",
"arxiv_id": "physics/0310048",
"authors": [
"Margarita F. Kondratieva",
"Sergey Yu. Sadov"
],
"categories": [
"physics.optics",
"physics.comp-ph"
],
"title": "Symbol of the Dirichlet-to-Neumann operator in 2D diffraction problems with large wavenumber",
"url": "https://arxiv.org/abs/physics/0310048"
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