Layered Medium And Sharp Regional Acoustic Scattering Problems

Acoustic scattering theory is a very meaningful subject in the field of math-ematical physics, and it is widely used in many applied sciences. Over the past decade, both in theory and in practical application, the acoustic scattering the-ory has been made significant development. On the basis of previous research, this paper make the following work:Firstly, we present the numerical methods of acoustic scattering in a ho-mogeneous medium of two layers with the boundary conditions of Dirichlet, Neumann and Impedance. Using the mix of single and double layer potential to approach the scattering wave and transmission wave. With the potential theory, we obtain boundary integral equations. Because the integral operator kernel function is logarithmic singular, we use Nystrom method to deal it.Secondly, the medium of two layers is promoted to m layers, then we get2m-1boundary integral equations. Using the same method to solve this prob-lem, and present several numerical examples to show the feasible and effective of the method.Finally, in the homogeneous medium, we give a method to solve the acous-tic scattering problem, which is impedance boundary condition with unsmooth region. Because of the kernel function of double potential is discontinuous, we need a transformation to solve it. For one corner, we give two transformations: exponential transformation and Kress transformation. For multiple corncs, we use multiple corners of Kress transformation formula.