Numerical Algorithm For Solving Acoustic Inverse Scattering In Non - Homogeneous Media

Inverse acoustic scattering problem is a kind of classical inverse problem in mathematical physics. It is widely applied in practice. In this thesis, we mainly discuss the numerical methods for solving the inverse acoustic scattering problem in inhomogeneous medium. First, we seek the approximate solution of the direct scattering problem by PML(perfectly matched layer)method. Then the far ?eld data are computed from the approximate solution and are taken as the measured data to obtain the inversion of the refractive index. We will give two inversion methods in this thesis, i.e. simpli?ed Newton method and modi?ed gradient method. Each iterative step in the ?rst method involves solving both a singular integral equation and an integral equation of the ?rst kind, we will employ a corrected trapzoidal rule and the Tikhonov regularization method to deal with the weak singularity and the illposedness respectively. The second method is a kind of optimization method which approximates the exact solution successively. At each step, the steepest descent directions and the minimizers of the residual are chosen as the modi?ed directions and step sizes. The numerical experiments are given at the end of this thesis,and the numerical results illustrate some feasibilities of the proposed methods.