On a Robin-type non-singular coupling scheme for solving the wave scattering problems

Abstract: 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.