ИСТИНА

The exterior problem for 2D Helmholtz equation is considered. An universal behaviour of the symbol of the Dirichlet-to-Neumann operator is noted in a number of exactly solvable cases in the limit of large wavenumbers. The observed asymptotic behaviour of the symbol apparently takes place also for general smooth convex and non-convex boundaries, as analytical and physical arguments and numerical study suggests. The connection of this conjecture with Kirchhoff approximation and a novel high-frequency numerical method are discussed.