Electrical and Electronics Engineering Faculty, Istanbul Technical University, Maslak 34469, Istanbul, Turkey.
J Acoust Soc Am. 2013 Apr;133(4):2097-104. doi: 10.1121/1.4794369.
An inverse acoustic scattering problem the main aim of which is to reconstruct the one-dimensional variation of the acoustical parameters of a spherical object is investigated. The problem is first formulated conventionally through a coupled system of integral equations, and then this system is reduced to one-dimensional form by using the orthogonality properties of spherical harmonics. The inverse problem is solved in an iterative fashion via classical Newton algorithm. Some numerical simulations are carried out to test the feasibility of the method as well as to see the effects of some parameters on the solution. It is shown that the method is very effective for the profiles having smooth variations provided that an appropriate initial guess is chosen. However, some of the classical disadvantages of the Newton type algorithms are also observed in numerical experiments which may limit the applicability of the method to a certain extent.
研究了一个逆声学散射问题，其主要目的是重建球形物体声学参数的一维变化。该问题首先通过一个积分方程组进行常规表述，然后通过球谐函数的正交性将该系统简化为一维形式。逆问题通过经典牛顿算法以迭代方式求解。进行了一些数值模拟，以测试该方法的可行性以及观察一些参数对解的影响。结果表明，只要选择适当的初始猜测，该方法对于具有平滑变化的轮廓非常有效。然而，在数值实验中也观察到牛顿型算法的一些经典缺点，这可能在一定程度上限制了该方法的适用性。
