Several Numerical Solution Of The Dirichlet Boundary Conditions The Problem Of Acoustic Scattering

Inverse problem can be understood on the grounds to seek the model and the reasons for some of the results. The inverse acoustic scattering problem is a typical Mathematics Physics inverse problem, and exists in a wide range of fields, such as remote sens-ing,medicine imaging and resources exploration of mineral. There are great difficulties in in-depth study of the inverse acoustic scattering problem,because it was realized that the inverse problem is ill-posed. In this paper,regularization method is introduced. The author pays more attentions to investigate the numerical solution for the direct acoustic scattering problem with the Dirichlet boundary condition, and the numerical recovering the shape of the obstacle region which is the inverse problem of the direct acoustic scattering problem with the Dirichlet boundary condition. Some satisfactory conclusions are also reached. The main woks of this paper are as follows:1.In order to improve the asymptotic convergence order of the regularized solution,a iterated Tikhonov regularization and a modified Tikhonov regularization are applied to solve the ill-posed integral equation of the first kind. Numerical experiments are presented for the integral equation with noisy data,and indicate that both methods are simple and effective.2.The numerical algorithms of the direct acoustic scattering problem with the Dirichlet boundary condition is studied,which is the foundation of the inverse acoustic scattering problem. Potential theory is used to transfer the exterior boundary value problem into the boundary integral equation of the first kind. A iterated Tikhonov regularization and a modified Tikhonov regularization are presented to solve the integral equation. Numerical results in two dimension are given. Compared with Nystr(o|¨)m method,both methods are accurate and simple to use.3.Based on the idea of the decomposition methods and Taylor series, the shape of an obstacle with the Dirichlet boundary condition is reconstructed. An approximation method is presented. Through the use of the Taylor expansion in the vicinity of the scatterer,the problem is directly reduced to the solution of a polynomial equation which is simpler to treat. Numerical experiments show the validity and practicality of this method.