A numerical approximation of the two-dimensional elastic wave scattering problem via integral equation method

In this paper, a numerical method is proposed to approximate the solution of a two-dimensional scattering problem of time-harmonic elastic wave from a rigid obstacle. By Helmholtz decomposition, the scattering problem is reduced to a system of Helmholtz equations with coupled boundary conditions. Then, we prove that the system of Helmholtz equations has only one solution under certain conditions, and propose an integral equation method to solve it numerically based on Tikhonov regularization method. Finally, numerical examples are presented to show the feasibility and effectiveness of the proposed method.