The Navier equation is the governing equation of elastic waves, and computing its solution accurately and rapidly has a wide range of applications in geophysical exploration, materials science, etc. In this paper, we focus on the efficient and high-precision numerical algorithm for the time harmonic elastic wave scattering problems from cornered domains via the boundary integral equations in two dimensions. The approach is based on the combination of Nystr\"om discretization, analytical singular integrals and kernel-splitting method, which results in a high-order solver for smooth boundaries. It is then combined with the recursively compressed inverse preconditioning (RCIP) method to solve elastic scattering problems from cornered domains. Numerical experiments demonstrate that the proposed approach achieves high accuracy, with stabilized errors close to machine precision in various geometric configurations. The algorithm is further applied to investigate the asymptotic behavior of density functions associated with boundary integral operators near corners, and the numerical results are highly consistent with the theoretical formulas.

翻译：纳维方程是弹性波的控制方程，其解的精确快速计算在地球物理勘探、材料科学等领域具有广泛应用。本文针对二维角域内时间谐和弹性波散射问题，基于边界积分方程提出了高效高精度数值算法。该算法结合了Nyström离散化、解析奇异积分与核分裂方法，实现了光滑边界的高阶求解，并通过递归压缩逆预条件（RCIP）方法拓展至角域弹性散射问题。数值实验表明，该算法在各种几何构型下均能实现高精度，稳定误差接近机器精度。进一步地，该算法被用于研究边界积分算子密度函数在角点附近的渐近行为，数值结果与理论公式高度吻合。