Key points are not available for this paper at this time.
Abstract This paper studies the time domain acoustic wave scattering problems of a bounded obstacle or a smooth open arc in the unbounded domain, where the obstacle has the smooth and closed boundary. Due to the potential theories, the first kind retarded single-layer potential boundary integral equations of the above problems can be obtained and they are solved by two steps, we get the temporal discretization by the convolution quadrature method firstly, and then the first kind boundary integral equations in space are solved by the quadrature method. Meanwhile, the scattered field can be computed in terms of the trapezoidal rule. The existence and uniqueness of the numerical solution are proved, the convergence of the approximate solution is also analysed and the error bound is got. The asymptotic expansion of the error in space shows that the convergence rate is O(h3). Moreover, the extrapolation algorithm is used to improve the accuracy of the numerical solution. The posteriori error estimate is also obtained, which is helpful for designing the self-adaptive algorithm. Some numerical experiments are implemented to show the effectiveness of our method.
Guo et al. (Fri,) studied this question.