利用远场模式的不完全数据反演声波阻尼系数  

Recovering the acoustic wave impedance coefficient from the incomplete far field pattern data

作　　者：麦宏晏[1] 王连堂[2] 

机构地区：[1]长安大学理学院,陕西西安710064 [2]西北大学数学系,陕西西安710069

出　　处：《纯粹数学与应用数学》2009年第3期566-572,共7页Pure and Applied Mathematics

基　　金：长安大学科技发展基金(07J05)

摘　　要：从阻尼边界条件声波散射问题的散射场远场模式的部分数据信息出发给出了反演声波阻尼系数的一种新方法,该问题既是非线性的又是不适定的,这里利用Tikhonov正则化方法将问题转化为一个最优化问题,成功地处理了第一类算子方程的不适定性及该问题的非线性性,给出了具体的数值方法并对其收敛性进行了严格地证明,数值结果表明该方法是非常准确且简单易行的.The method we are considering in this article is a novel method to recover the impedance coefficient from the knowledge of the incomplete far field pattern data of the scattered wave for the time-hormonic acoustic scattering problem. It is transformed into an optimization problem employing Tikhonov regularization method in order to solve the ill-posedness of the equation of the first kind and its nonlinearity successfully. Numerical method is given and the convergence of the method is rigorously proven. Numerical examples are shown that this method is both accurate and simple to use.

关 键 词：阻尼边界条件 远场模式 反演 部分数据 

分 类 号：O175.29[理学—数学]