Theoretical Analysis And Numerical Algorithm For A Class Of Rough Surface Compound Scattering Problems

In this paper,the scattering problem of a class of obstacles embedded in a two-layer medium in two-dimensional space is studied.The two-layer medium is separated by an unbounded rough surface,and the obstacles are embedded above the rough surface.Two scattering models are discussed respectively.The first model is the composite acoustic scattering problem of acoustic hard obstacle and rough surface.Given a point source,an obstacle and an unbounded rough surface,the scattering problem is to solve the wave field distribution in space.Firstly,the scattering problem model with the second boundary condition,the boundary integral equation equivalent to the scattering problem is established by using the indirect boundary integral equation method.Then,by using the variational theory and Fredholm's alternative theorem,we study the well-posedness of the solution,that is,its existence and uniqueness.Finally,the integral equation is numerically discretized by the method of moments.The second model is the problem of composite sound scattering between soft obstacles and rough surfaces.Firstly,for the scattering problem model with the first kind of boundary conditions,the boundary integral equation equivalent to the scattering problem is established by using the direct boundary integral equation method.Then,the well-posedness is studied by using variational theory and Fred-holm's alternative theorem.