This paper studies a non-singular coupling scheme for solving the acoustic and elastic wave scattering problems and its extension to the problems of Laplace and Lam\'e equations and the problem with a compactly supported inhomogeneity is also briefly discussed. Relying on the solution representation of the wave scattering problem, a Robin-type artificial boundary condition in terms of layer potentials whose kernels are non-singular, is introduced to obtain a reduced problem on a bounded domain. The wellposedness of the reduced problems and the a priori error estimates of the corresponding finite element discretization are proved. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

翻译：本文研究了一种用于求解声波与弹性波散射问题的非奇异耦合格式，并简要讨论了该方法在Laplace方程、Lamé方程以及紧支撑非均匀性问题中的推广。基于波散射问题的解表示，引入了一种以层势表示的Robin型人工边界条件（其核函数为非奇异函数），从而在有界域上获得简化问题。证明了简化问题的适定性以及相应有限元离散的先验误差估计。数值算例验证了该方法的精确性与有效性。