求解二维多区域声波传播问题的一种边界元方法

针对多区域中声波的传播问题,其中每个散射区域的介质是相同的,将散射区域内的声波用一种单双层混合位势的形式来表示,再应用Green定理表示出外部介质区域中的声波,并形成相应的边界积分方程.如果区域个数为M时,传统的边界元方法最终将形成2M个边界积分方程并对应2M个未知函数,而本文的边界元方法最终只形成M个边界积分方程以及对应M个未知函数,从而使得求解的方程和未知数的个数都减少了一倍.最后,通过对数值算例的求解,验证了该方法的可行性及精确性.

A boundary element method for solving acoustic transmission problem with multiple domains

In this paper,we discuss the acoustic transmission problem in multiple domains. We denote the acoustic in the scattering domains in the form of combined double and single-layer potentials and each domain＇s mediums is the same, and then get the acoustic in the outer domain and boundary integral equation by Green theory. The traditional boundary element method will eventually form 2M boundary integral equations with 2M unknowns if there are M domains. However, we obtain a set of M equations with M unknowns and half of the equations can be reduced by applying the method in this paper. Finally, the numerical examples were given to test the accuracy and feasibility of the method