On Evaluation of the Diffraction Coefficients for Arbitrary "Nonsingular" Directions of a Smooth Convex Cone

Abstract

Diffraction coefficients are fundamental objects determining principal amplitudes in asymptotic expansions for a general high-frequency diffraction problem and are to be found from an associated problem. For a class of canonical problems of plane wave diffraction by an arbitrarily shaped smooth convex cone (formulated as a boundary value problem for the Helmholtz equation with Dirichlet or Neumann boundary conditions), we develop a method for evaluating the diffraction coefficients in arbitrary nonsingular directions, i.e., in all the directions where they are well defined. The approach builds further on the analytic representations of V. P. Smyshlyaev [Wave Motion, 12 (1990), pp. 329--339], and the constructions of V. M. Babich, D. B. Dement'ev, and B. A. Samokish [Wave Motion, 21 (1995), pp. 203--207], who have previously developed a method for calculating the diffraction coefficients in certain restricted directions, for which an integral over a complex contour determining the diffraction...