Boundary Points And A Modified Regularization Method To Solve The Acoustic Scattering Problem

The inverse problem is a comprehensive academic research, the acous-tic scattering as an important branch of the inverse problem of mathematical physics, with the inverse problem of the capture of two decades, the study of wave scattering has become more sophisticated, acoustic scattering from the initial finite element method to the boundary element method is now more opti-mized. Get a great development, and to make use of it, tend to be widely, mainly involves in the groundwater exploration, archaeological discovery, material with-out injury flaw detection and medical CT, radar, and other fields. This article mainly do the following work:chapter1:Introduction condensed to ask the relevant knowledge, as well as some of its fields of application, and then the sound waves scattering problem are introduced and the mathematical model.Chapter2:of sound waves in the scattering potentials theory give a specific instructions, and Laplace equation of T、K、S、K’ the four types of operators are given a specific definition and overtaken by the specific derivation of their parameters.Chapter3:using potential theory to the wave scattering problem is trans-formed into a boundary integral equation, and then using the singular function to build new formula the second category of weak singular equation. And giveing the Dirichlet boundary integral of a sound wave scattering problem solving method, with two dimensional space algorithm for example. The results show that it has better precision.Chapter4:through the regularization method is introduced, using single potentials theory sound waves scatter the problem into the first class boundary integral equation, and by using the improved Tikhonov regularization method to solve sound waves to scatter, finally, giving the example, this results show the feasibility and effectiveness of the he and high precision.