An Efficient Treatment of Sound Diffraction by Arbitrary Obstacles with Angles

Abstract

The problem under consideration arises in ultrasonic evaluation of modern elastic materials, in the case when potential defects may contain sharp corners on their boundary. The paper is concerned with a two-dimensional diffraction of a point source acoustic wave by arbitrary defect containing a finite number of angles. By Boundary Element Method (BEM), the problem is reduced to the integral equation, over the boundary of the obstacle. We apply a numerical approach, with a discretization of the boundary curve. Then the main Boundary Integral Equation (BIE) is converted to the system of linear algebraic equations (SLAE). Two specific approaches are used to improve the precision of the solution. The first one is based on two different meshes—near and outside a small neighbourhood of the corners. The second one is to take into account the angles, which consists of explicit analytical representation for those matrix elements connected with the nodes closest to the angles. This idea based on a small argument asymptotics of the Hankel function, in a combination with the first advanced method, demonstrates good precision, including small vicinity of the angles as well. As an example, we test the proposed algorithm in the case of diffraction by a polygon with straight-line sides.