Analysis And Calculation Of The Scattering Problem Of Multiple Obstacles Below The Sea Surface

In this paper,the problem of scattering by multiple obstacles below the sea surface in two dimensions is investigated from both theoretical analysis and numerical calculation.By analyzing the properties of the scattering problem and using the Helmholtz equation with different boundary conditions and the radiation conditions at infinity,a mathematical model of the scattering problem from a multi-barrier body below the sea surface is established.Based on the potential theory,the integral representations satisfied by the sites in different regions and the boundary integral equations satisfied by the density function on the boundary are obtained by using the indirect integral equation method.Further,the potential operator is introduced and its properties are analyzed to represent the system of boundary integral equations in the form of an operator matrix.The equivalence of the system of differential equations and the system of boundary integral equations is proved,and the uniqueness for the solution of the scattering problem is obtained.To realize the numerical calculation,a discrete numerical format is constructed for the established system of boundary integral equations,and the convergence of the numerical solution is proved.Based on the above theoretical analysis,numerical examples of the scattering problem are designed to obtain numerical results for scattering problem of multiple obstacles below the sea surface.