刚性目标形状反演的一种非线性最优化方法

Numerical Method for the Shape Reconstruction of a Hard Target

发展了从声散射场的远场分布的信息来再现声刚性目标形状反问题的一种非线性最优化方法,它是通过独立地求解一个不适定的线性系统和一个适定的非线性最小化问题来实现的· 对反问题的非线性和不适定性的这种分离式数值处理,使所建立方法的数值实现是非常容易和快速的,因为在确定声刚性障碍物形状的非线性最优化步中,只需求解一个只有一个未知函数的小规模的最小平方问题· 该方法的另一个特别的性质是,只需要远场分布的一个Fourier系数。

A nonlinear optimization method was developed to solve the inverse problem of determining the shape of a hard target from the knowlegde of the far_field pattern of the acoustic scattering wave,it was achieved by solving independently an ill_posed linear system and a well_posed minimization problem.Such a separate numerical treatment for the ill_posedness and nonlinearity of the inverse problem makes the numerical implementation of the proposed method very easy and fast since there only involves the solution of a small scale minimization problem with one unknown function in the nonlinear optimization step for determining the shape of the sound_hard obstacle.Another particular feature of the method is that it can reproduce the shape of an unknown hard target efficiently from the knowledge of only one Fourier coefficient of the far_field pattern.Moreover,a two_step adaptive iteration algorithm was presented to implement numerically the nonlinear optimization scheme.Numerical experiments for several two dimensional sound_hard scatterers having a variety of shapes provide an independent verification of the effectiveness and practicality of the inversion scheme.