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求解多层介质中声波传播问题的一种边界元方法

岳雪莲, 王连堂, 孟文辉   

  1. 西北大学数学系, 西安 710000
  • 收稿日期:2012-05-16 出版日期:2013-03-15 发布日期:2013-03-12

岳雪莲, 王连堂, 孟文辉. 求解多层介质中声波传播问题的一种边界元方法[J]. 数值计算与计算机应用, 2013, 34(1): 75-80.

Yue Xuelian, Wang Liantang, Meng Wenhui. A BOUNDARY ELEMENT METHOD FOR SOLVING ACOUSTIC TRANSMISSION PROBLEM WITH MULTI-LAYERED DOMAIN[J]. Journal of Numerical Methods and Computer Applications, 2013, 34(1): 75-80.

A BOUNDARY ELEMENT METHOD FOR SOLVING ACOUSTIC TRANSMISSION PROBLEM WITH MULTI-LAYERED DOMAIN

Yue Xuelian, Wang Liantang, Meng Wenhui   

  1. Department of Mathematics, Northwest University, Xi'an 710000, China
  • Received:2012-05-16 Online:2013-03-15 Published:2013-03-12
针对多层介质中声波的传播问题, 将其中偶数(或奇数)层内的声波用一种单双层混合位势的形式来表示, 再应用Green定理表示出其余层的声波并形成相应的边界积分方程.如果区域有M层时, 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, 而应用上述方法求解该问题时, 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.
To solve the acoustic transmission problem in multi-layered, it represents the acoustic on the even(or odd) layer in the form of combined double and single-layer potentials, and then gets the acoustic on the rest layer and boundary integral equation by Green theory.The traditional boundary element method will eventually form 2M boundary integral equations with domain of M layers, and half of the equations can be reduced by applying the method above. Finally, the numerical examples were given to test the accuracy and feasibility of the method.

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