Quadrature method for solving the boundary integral equations of elastic wave scattering problems

This paper solves elastic wave obstacle scattering problem in the unbounded domain, where the obstacle has the smooth and closed boundary. Based on the Helmholtz decomposition, the original scattering problem is converted to the coupled boundary value problem (BVP) of the Helmholtz equations. The boundary integral equations (BIEs) of this BVP are obtained by the potential theories. The kernels of the BIEs in this paper are only of Cauchy singularity and they are divided into two parts, the one is a smooth kernel and the other one is the Hilbert kernel multiplied by a smooth part. Due to the quadrature method, we solve the above BIEs numerically, meanwhile, the existence and uniqueness of the approximate solution are proved from the theory of collectively compact convergence, and the error estimate is given. Numerical experiments are carried out to show the effectiveness of our method.