Boundary Integral Method For Acoustic Inverse Scattering Problem

Acoustic scattering theory is widely applied to radar,sonar,noise barrier design,atmospheric particle scattering,geological survey,medical diagnosis,etc.The mathematical problem corresponding to the acoustic scattering problem is to solve the Helmholtz equation.In this paper,we introduce the procedure of solving the Helmholtz equation by using the boundary integral method and give the concrete derivation process.Then we develop a two-steps procedure to solve the acoustic scattering direct problem and describe two discrete methods.In one method,we split the integral kernel in a special way and use the Nystr?m method for discrete integration.In another method,the discreteness of the integral kernel can be directly divided into diagonal and non-diagonal terms.Non-diagonal elements can be calculated directly and diagonal elements of the equation can be solved by Green's identity method.The numerical experiment is carried out on the direct scattering problem.Then,for the three different boundary curves,we respectively give the corresponding incident wave,scattering wave and the total wave.It intuitively reflect the scattering of sound waves.We use Newton iterative method to solve the inverse problem of acoustic scattering.In discrete case,we use regularization method to obtain the stable boundary increment and ensure the stability of approximate solution.