A numerical solution of the scattering problem for acoustic waves by a two-sided crack in 2-dimensional space.

*(English)*Zbl 1249.74063Summary: The wave scattering problem at a crack \(\Gamma\) in \(\mathbb R^2\) with impedance type boundary is considered. This problem models the diffraction of waves by thin two-sided cylindrical screens. A numerical method for solving the problem is developed. The solution of the problem is represented in the form of the combined angular potential and the single-layer potential. The linear integral equations satisfied by the density functions are derived for general parameterized arcs. The weakly singular integrals and the Cauchy singular integral arising from these equations are computed using a highly accurate scheme with a truncation error analysis. The advantage of the scheme proposed in this paper is, on one hand, the fact that we do not need the analyticity properties of the crack and we allow for different complex valued surface impedances in both sides of the crack; and on the other hand, we avoid hyper-singular integrals. Numerical implementations showing the validity of the scheme are presented.