Researches On The Uniqueness And Numerical Solution Of The Reconstruction Of A Ball With A Single Incoming Wave

The inverse scattering problem of acoustic wave is a kind of typical mathematical physics inverse problem,which has a wide range of applications in real life,such as Geological prospecting and Sonar Technology,Because of its high nonlinearity and ill-posedness,the theory and computation of the inverse problems are difficult.Therefore,to solve these problems has become the direction of many scientists and engineers.This paper only considers acoustic inverse scattering problem,especially the acoustic inverse scattering problem of sphere obstacle.Firstly,this paper introduces the theory of Helmholtz equations,then by using the Bessel function,the spherical harmonic function and Jacobi-Anger expansion to obtain the series form solution of the direct scattering problem of a ball,we prove the translation property of the far field pattern by the series expansion form of the radiation solution directly.For a sphere obstacle with impedance boundary condition(with unknown impedance coefficient),we prove that it can be determined by the far-field pattern corresponding to an incident plane wave.we also study the numerical solution of the inverse scattering prob lems of balls in two dimension.in order to obtain the far-field pattern of the direct acoustic obstacle scattering problem,we use the integral equation method and the series expansion method to solve the two-dimensional acoustic scattering problem of sphere obstacle.Then,we improve the Range test method with the idea of shrinking the range of the center of the ball to obtain the position of the sphere,and numerical experiments show the validity of the algorithm.