可穿透障碍散射问题的数值方法

摘要

By using a Trefftz class algorithm,we gave a numerical method for solving the scattering problem of a class of time-harmonic wave by penetrable obstacle.The method was based on the leastsquares algorithm,Fourier-Bessel functions were used to approximate the local state of the field,and a model was established by using multipole expansion to approximate the behavior of scattered field at infinity.The results show that the method is appropriate for the scatters whose domain may be multiple or even multi-connected.Moreover,it does not need to truncate the space,and high accuracy can be achieved by adding the number of the basis functions in the coarse mesh.Numerical examples are carried out to illustrate the effectiveness of the proposed algorithm.%利用Trefftz类算法,给出一种数值求解一类时谐波被可穿透障碍散射问题的方法.该方法基于最小二乘算法,采用Fourier-Bessel函数近似场的局部性态,并利用多极展开逼近散射场在无穷远处的性态建立模型.结果表明,该方法适用于多个散射体情形以及散射体为多连通区域情形,并且无需将空间截断,在粗糙网格下通过增加基底数目即可达到较高精度.数值算例验证了算法的有效性.