Simultaneous study of the diffraction by a 2D-convex obstacle through boundary layer method and microlocal analysis

Abstract

In this paper we consider the high frequency diffraction of electromagnetic waves by a strictly convex obstacle. We restrict ourselves to the case of an obstacle in 2D and to the diffraction of a TE or TM wave.

The aim of this paper is to present simultaneously with the same notations, unknowns and special functions the boundary layer analysis of this problem with stretched variables using the intuition of the solutions and the microlocal analysis way of construction of an adapted parametrix. We concentrate on the case of diffraction, i.e. studying the representation of a creeping wave on the boundary, which occurs in the case of the study of a glancing point.

We use both methods to derive the exact solution near a diffractive point, obtaining results in terms of suitable Airy functions.