Solving The Three Iterative Methods For Acoustic Scattering Problems

Inverse acoustic scattering problems play an important role in mathematical physics equation inverse problems. It has a wide range of applications in our life such as sonar, radar imaging technology. These are related to the methods for solving inverse acoustic scattering problems. That is based on the measured acoustic scattering data to reconstruct the shape or infer the physical properties of an object.The paper mainly describes three different iteration methods for solving inverse problems.Firstly, by using the single layer potential solving the Neumann inverse problem of a closed boundary, it introduces the first iteration scheme. The method gives initial boundary and get the corresponding density function by solving the boundary condition equation. Then solve the linearized equation with the increment of the boundary and far field pattern using the density function obtained. Using regularization method solve the increment in order to update the boundary and form iteration. Secondly, the paper introduces the second iteration scheme by the case of a Dirichlet open arc. In the charper, the first part uses the first iterative method recovering the open arc and gives contrast figures using one incident plane wave and more than one incident field. Then the late part gives the second iteration method. The method gives initial boundary and get the density function by solving the boundary condition equation. Then the non-linear equations with initial boundary and the density function obtained are replaced by the linearized equations. Using the minimization method deal with the linear equations by regularization in order to update the boundary and form iteration. The last part of the paper presents a method called hybird iteration method. It solves the Dirichlet inverse problem of a closed boundary by using the single layer potential. It gives initial boundary and get the corresponding density function by using regularization dealing with the far field pattern equation. In order to obtain the increment, solve the linearized equation with the initial boundary and the corresponding density function obtained. Then update the boundary and form iteration. For these three iterative methods, the numerical examples are given in the paper. Three methods are effective through the reconstruction figures given in the paper.