阻尼边界条件下声波散射的一个逼近方法  

Approximation method for acoustic scattering with impedance condition

作　　者：麦宏晏[1,2] 王连堂[1] 

机构地区：[1]西北大学数学系 [2]长安大学理学院,陕西西安710064

出　　处：《长安大学学报（自然科学版）》2005年第1期105-107,共3页Journal of Chang’an University(Natural Science Edition)

基　　金：陕西教育厅自然科学基金项目(2002A10)

摘　　要：将阻尼边界条件下声波散射问题转化为求解一个最小二乘法问题,将散射波表示为单层位势,该问题满足拟牛顿法的收敛条件,采用拟牛顿法得到逼近散射波的傅立叶级数的系数,并根据散射波与其远场模式之间的关系求得散射波的远场模式。通过给出二维空间的具体的数值计算实例与已有的求解积分方程的方法比较,该方法计算量小且计算速度快,而得到的精度却是一样的。The acoustic scattering with impedance boundary condition is transferred into solving a problem in a minimum norm sense. The scattered field is represented as the acoustic single-layer potential. This problem is satisfied with the convergence condition of the Quasi-Newton algorithm. The Fourier coefficient of the scattered wave is got by the Quasi-Newton algorithm. The far field pattern of the scattered wave is solved employing the relation between the far field and the scattered wave. Numerical method in two dimensions is given. Compared with the boundary integral equations of the second kind method, the numerical rate of this method is faster than that of the former, but has the same accuracy.

关 键 词：HELMHOLTZ方程 声波 散射 阻尼边界条件 远场模式 逼近方法 

分 类 号：O174.41[理学—数学]