On An Hybrid Technique For Combining The Uniform Theory Of Diffraction With Finite Boundary Elements

Abstract

The resolution of diffraction problems of incident waves through an obstacle is generally based on classical numerical methods for the calculations in low frequency ranges, and on the asymptotic ones for the high frequency calculations. However, it is sometimes difficult to use only one resolution method, when the diffracting object presents simultaneously small and large dimension zones with respect to the wave length. Therefore, it is useful to couple the two methods, numerical and asymptotic, for treating the problem correctly. This work treats diffraction problem of a monochromatic plane wave, incident on a rigid obstacle presenting a singularity. Initially, the pressure field is calculated in all space points using Uniform Theory of Diffraction, which corrects the results of the Geometrical Theory of Diffraction through the light-shadow transition zone and in the vicinity of the caustics, and which reduces to the same elsewhere. Secondly, the pressure field is calculated using the boundary finite elements.